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The use of graph theory is prevalent in the field of network design, whereby it finds utility in several domains such as the development of integrated circuits, communication networks, and transportation systems. The comprehension of partition dimensions may facilitate the enhancement of network designs in terms of efficiency and reliability. Let VG be a vertex set of a connected graph and S⊂VG, the distance between a vertex v and subset S is defined as dv,S=mindv,xx∈S. An k-ordered partition of VG is Rp=Rp1,Rp2,…,Rpk and the identification code of vertex v with respect to Rp is the k-tuple rvRp=dv,Rp1,dv,Rp2,…,dv,Rpk. The k-partition Rp is said to be a partition resolving if rvRp, ∀v∈VG are distinct. Partition dimension is the minimum number k in the partition resolving set, symbolized by pdG. In this paper, we considered the families of graph named as Toeplitz network, and proved that the partition dimension of Tnt1,t2, where t1=2,3, and gcdt1,t2=1 is constant.

Chemical graph theory, a branch of computational and applied mathematics, covers a very wide range of topics. As a result, the world of applied sciences heavily relies on graph theory. The concept of partition dimension has significant importance in the field of chemical graph theory. Although certain graphs have bounded partition dimensions, a graph’s partition dimension may be constant. In this study, we look at two alternative chemical structures made of an octagonal grid: nanosheets and nanotubes. We determined the partition dimension of an octagonal grid-generated nanosheet to be 3, and the partition dimension of a nanotube to be limited from 4.

For a simple graph G=(V,E) with the vertex set V(G) and the edge set E(G), a vertex labeling φ:V(G)→{1,2,…,k} is called a k-labeling. The weight of an edge under the vertex labeling φ is the sum of the labels of its end vertices and the modular edge-weight is the remainder of the division of this sum by |E(G)|. A vertex k-labeling is called a modular edge irregular if for every two different edges their modular edge-weights are different. The maximal integer k minimized over all modular edge irregular k-labelings is called the modular edge irregularity strength of G. In the paper we estimate the bounds on the modular edge irregularity strength and for caterpillar, cycle, friendship graph and n-sun we determine the precise values of this parameter that prove the sharpness of the lower bound.

Cancer is a disease that causes abnormal cell formation and spreads throughout the body, causing harm to other organs. Breast cancer is the most common kind among many of cancers worldwide. Breast cancer affects women due to hormonal changes or genetic mutations in DNA. Breast cancer is one of the primary causes of cancer worldwide and the second biggest cause of cancer-related deaths in women. Metastasis development is primarily linked to mortality. Therefore, it is crucial for public health that the mechanisms involved in metastasis formation are identified. Pollution and the chemical environment are among the risk factors that are being indicated as impacting the signaling pathways involved in the construction and growth of metastatic tumor cells. Due to the high risk of mortality of breast cancer, breast cancer is potentially fatal, more research is required to tackle the deadliest disease. We considered different drug structures as chemical graphs in this research and computed the partition dimension. This can help to understand the chemical structure of various cancer drugs and develop formulation more efficiently.

Traumatic lumbar hernias are a rare subset of abdominal wall hernias encountered following blunt trauma to the abdomen. These are more commonly being found due to the increased use of advanced imaging. Three cases of traumatic lumbar hernias were identified at our institution from 2021 to 2022, one of which underwent delayed repair. The second case resulted in the resolution and healing of the defect within 6 weeks of presentation, and the third was lost to follow up. Acute repair of lumbar hernias might be indicated during the repair of other intra-abdominal injuries. Delayed repair allows for a laparoscopic approach or open repair via flank incisions. Delay in asymptomatic patients may also result in fibrosis and scarring and may resolve the defect. Fixation of mesh to adjacent bony structures may be needed, and adequate sub-lay dissection for mesh placement particularly for larger defects. Consider delaying the repair of traumatic lumbar hernias in asymptomatic to minimally symptomatic patients if no other abdominal surgery was warranted at the time of presentation.

Abstract Background Proline (Pro) and hydrogen peroxide (H2O2) play a critical role in plants during drought adaptation. Genetic mapping for drought-induced Pro and H2O2 production under field conditions is very limited in crop plants since their phenotyping with large populations is labor-intensive. A genome-wide association study (GWAS) of a diversity panel comprised of 184 bread wheat cultivars grown in natural field (control) and rain-out shelter (drought) environments was performed to identify candidate loci and genes regulating Pro and H2O2 accumulation induced by drought. Results The GWAS identified top significant marker-trait associations (MTAs) on 1A and 2A chromosomes, respectively for Pro and H2O2 in response to drought. Similarly, MTAs for stress tolerance index (STI) of Pro and H2O2 were identified on 5B and 1B chromosomes, respectively. Total 143 significant MTAs were identified including 36 and 71 were linked to drought and 2 and 34 were linked to STI for Pro and H2O2, respectively. Next, linkage disequilibrium analysis revealed minor alleles of significant single-markers and haplotypes were associated with higher Pro and H2O2 accumulation under drought. Several putative candidate genes for Pro and H2O2 content encode proteins with kinase, transporter or protein-binding activities. Conclusions The identified genetic factors associated with Pro and H2O2 biosynthesis underlying drought adaptation lay a fundamental basis for functional studies and future marker-assisted breeding programs.

This research aims to describe and interpret forms of interreligious rituals in primary schools. Researchers also look at children's religious expressions in practicing interreligious rituals and their contribution as learning resources in building a sense of togetherness in schools. This study uses a qualitative-phenomenological approach with data collection interviews, observations, and documentation. The results showed that children's religious rituals were taught in and outside the classroom. They practice with teachers of the same religion in class, but outside the classroom, they practice with students of other religions as spectators. Therefore, religious rituals that can be communicated socially are celebrated. Interreligious rituals do not make children and parents experience theological fear but can become a source of learning to recognize and respect other religious rituals. The ritual expression is an expression of harmony and togetherness because they can cooperate in celebrating their respective religious rituals.

ABSTRACT Aspergillus fumigatus is a respiratory pathogen, which has the potential to cause brooder pneumonia in poultry chicks and aspergillosis in birds and farmers. Frequent and irrational use of antifungals has led to the development of resistance in the fungal species. The present study aimed to evaluate the antifungal activity of essential oils (EOs) from four different spices against multi-drug resistant (MDR) A. fumigatus isolated from 40 poultry feed samples. Twenty fungal isolates were identified to be A. fumigatus based on the macroscopic and microscopic characteristics, which were confirmed by targeting and amplifying the species-specific rodA gene (313 bp). Five (5/20) isolates were found to be MDR by the disk diffusion method. EOs were tested as an alternative strategy for 5 MDR isolates of A. fumigatus. Clove EO provided better activity by 6 log10 reduction for 30-90 min exposure as compared to other EOs, therefore, shortlisted for well-diffusion and minimum inhibitory concentration (MIC) method. Clove EO provided promising results as compared to fluconazole, amphotericin B, ketoconazole, nystatin and voriconazole as its mean ZOI (39.6 ± 6.34) were better than all other commercial antifungals (p< 0.001). Mean MIC was reported to be 0.195 ± 0.11 µl/ml. Safety testing of the EO produced 74-82% cell viability for the range of 0.390 - 0.097 µl/ml as compared to DMSO. Findings of the present study highlight that clove EO can be source of a good therapeutic agent for infections of MDR isolates of A. fumigatus.

Objective This study was conducted to assess the knowledge and attitude of healthcare workers towards basic life support (BLS) in Khyber Teaching Hospital, Peshawar, and to investigate the factors affecting them.Design Cross-sectional study.Setting This study was carried out in a tertiary care hospital in Peshawar, Pakistan.Participants 201 healthcare professionals were recruited for this study through simple convenience sampling which included house officers (HOs), trained medical officers, postgraduate residents, professors, specialty registrars and nurses. Healthcare professionals who were reluctant to give consent were excluded from the study.Results Among the chosen participants, only 16.4% had good knowledge whereas 63% had a good attitude towards BLS. Knowledge of participants was found to be positively associated with less time elapsed between the training sessions (p=0.041). On the other hand, factors such as age(p=0.004), designation (p=0.05), number of BLS sessions attended (p=0.012) and the time elapsed since the last BLS session attended (p=0.015), were positively associated with the attitude of healthcare professionals.Conclusion The level of knowledge and attitude towards BLS by healthcare professionals was suboptimal. Those individuals who had attended BLS training sessions frequently had better knowledge and attitude as compared with their counterparts.

هدفت هذه الدراسة إلى قياس وتحليل مدد انجاز الأهداف المخطط لها والفعلية، فضلا عن تحليل مدى تباين الأهداف المنجزة من ناحية التخصيصات، وتحديد الخصائص الرئيسية للمشاريع والبرامج الحكومية، والتوصية بكيفية استخدامها لتحسين الأداء، ولعدم وجود أهداف واضحة ومحددة تم تبنيها من قبل إدارة المحافظة عند تنفيذ عملية التطوير. فضلا عن عدم الاعتماد على مؤشرات الأداء التي تحقق العدالة المالية والزمنية في توزيع مخصصات برنامج التنمية الاقليمي. ولغرض تحليل الخيارات المتاحة لتنفيذ مشاريع تنمية الأقاليم تم تحليل (5) قطاعات خدمية من اصل 12 قطاع في محافظة (كربلاء المقدسة) بالاعتماد على البيانات والتقارير الرسمية الصادرة من الدوائر المختصة والمعنية بتنفيذ مشاريع التنمية، فضلا عن قواعد البيانات والمؤشرات التنموية الصادرة من قسم الجهاز المركزي الاحصائي وقسم التنمية البشرية في وزارة التخطيط العراقية للمدمة من 2008 الى 2022 م. وبعد مقارنة جميع الخيارات المتاحة في كل مشروع من مشاريع هذه القطاعات، تبين أنه لم يتم مراعاة التخصيصات والزمن في تنفيذ المشاريع الخاصة بكل منها، حيث إن بعض التخصيصات المقدرة للمشاريع بعيدة عن التكاليف الفعلية، فضلا عن عدم وجود تحكم بوقت بدء تنفيذ المشروع وانهاؤه، أي إنه لا توجد جدولة مدروسة للمشاريع التنموية، ولغرض الحصول على نتائج حقيقية ودقيقة تغني الجانب العملي للدراسة الحالية فقد تم التحليل الكمي للبيانات وفق معياري (المدد والتخصيصات المالية) بالاستناد على الأوساط الحسابية والأشكال البيانية وكذلك استخدام معامل جيني (Gini Coefficient) في تحليل البيانات الخاصة بالقطاعات الداخلة ضمن اطار البحث والتي أظهرت تلكؤ وتعثر واضح في تنفيذ المشاريع والافتقار إلى التخطيط والتقدير الزمني والمالي في أغلب مشاريع القطاعات التي اتخذت كعينة لهذا البحث، فضلا عن عدم وجود عدالة في توزيع الاستثمار بين القطاعات الخدمية.

Key Clinical Message Use of pacemakers has increased in recent years, and they have become the premier treatment option for several arrhythmias. However, they are not without risk; this case report aims to show the importance of follow‐up and adherence to guidelines, and methods to diagnose a life‐threatening complication.

Radiation-associated cardiovascular disease, an increasingly recognised disease process, is a significant adverse effect of radiation therapy for common malignancies that involve the chest, and include lymphomas, lung, mediastinal and breast cancers. Two factors contribute to the increasing incidence of radiation-associated cardiovascular disease: advances in malignancy detection and the improved survival of cancer patients, by which many symptoms of radiation-associated cardiovascular disease, specifically radiation-associated arrhythmias, present years and/or decades following initial radiotherapy. We present a focused overview of the currently understood pathophysiology, prevalence and management strategies of radiation-associated arrhythmias, which include bradyarrhythmias, tachyarrhythmias and autonomic dysfunction.

Studying soil composition is vital for agricultural and edaphology disciplines. Presently, colorimetry serves as a prevalent method for the on-site visual examination of soil characteristics. However, this technique necessitates the laboratory-based analysis of extracted soil fragments by skilled personnel, leading to substantial time and resource consumption. Contrastingly, sensor techniques effectively gather environmental data, though they mostly lack in situ studies. Despite this, sensors offer substantial on-site data generation potential in a non-invasive manner and can be included in wireless sensor networks. Therefore, the aim of the paper is to develop a low-cost red, green, and blue (RGB)-based sensor system capable of detecting changes in the composition of the soil. The proposed sensor system was found to be effective when the sample materials, including salt, sand, and nitro phosphate, were determined under eight different RGB lights. Statistical analyses showed that each material could be classified with significant differences based on specific light variations. The results from a discriminant analysis documented the 100% prediction accuracy of the system. In order to use the minimum number of colors, all the possible color combinations were evaluated. Consequently, a combination of six colors for salt and nitro phosphate successfully classified the materials, whereas all the eight colors were found to be effective for classifying sand samples. The proposed low-cost RGB sensor system provides an economically viable and easily accessible solution for soil classification.

Turbidity is one of the crucial parameters of water quality. Even though many commercial devices, low-cost sensors, and remote sensing data can efficiently quantify turbidity, they are not valid tools for the classification it. In this paper, we design, calibrate, and test a novel optical low-cost sensor for turbidity quantification and classification. The sensor is based on an RGB light source and a light detector. The analyzed samples are characterized by turbidity values from 0.02 to 60 NTUs, and have four different sources. These samples were generated to represent natural turbidity sources and leaves in the marine areas close to agricultural lands. The data are gathered using 64 different combinations of light, generating complex matrix data. Machine learning models are compared to analyze this data, including training, validation, and test datasets. Moreover, different alternatives for data preprocessing and feature selection are assessed. Concerning the quantification of turbidity, the best results were obtained using averaged data and principal components analyses in conjunction with exponential gaussian process regression, achieving an R2 of 0.979. Regarding the classification of the turbidity, an accuracy of 91.23% is obtained with the fine K-Nearest-Neighbor classifier. The cases in which data were misclassified are characterized by turbidity values lower than 5 NTUs. The obtained results represent an improvement over the current solutions in terms of turbidity quantification and a completely novel approach to turbidity classification.

The book explores how Pakistan’s changing geopolitics affected Afghans’ livelihoods and their sense of identity and belonging during four decades of violence in Afghanistan through oral histories of Afghan migrants in Karachi and Peshawar, two of Pakistan’s main cities.

Abstract Background COVID-19 related stigma has been identified as a critical issue since the beginning of the pandemic. We developed a valid and reliable questionnaire to measure COVID-19 related enacted stigma, inflicted by the non-infected general population. We applied the questionnaire to measure COVID-19 related enacted stigma among Tehran citizens from 27 to 30 September 2020. Methods A preliminary questionnaire with 18 items was developed. The total score ranged from 18 to 54; a higher score indicated a higher level of COVID-19 related stigma. An expert panel assessed the face and content validity. Of 1637 randomly recruited Tehran citizens without a history of COVID-19 infection, 1064 participants consented and were interviewed by trained interviewers by phone. Results Item content validity index (I-CVI), Item content validity ratio (I-CVR), and Item face validity index (I-FVI) were higher than 0.78 for all 18 items. The content and face validity were established with a scale content validity index (S-CVI) of 0.90 and a scale face validity index (S-CVI) of 93.9%, respectively. Internal consistency of the questionnaire with 18 items was confirmed with Cronbach’s alpha of 0.625. Exploratory factor analysis revealed five latent variables, including “blaming”, “social discrimination”, “dishonor label”, “interpersonal contact”, and “retribution and requital attitude”. The median of the stigma score was 24 [25th percentile: 22, 75the percentile: 28]. A large majority (86.8%) of participants reported a low level of stigma with a score below 31. None of the participants showed a high level of stigma with a score above 43. We found that the higher the educational level the lower the participant’s stigma score. Conclusion We found a low level of stigmatizing thoughts and behavior among the non-infected general population in Tehran, which may be due to the social desirability effect, to the widespread nature of COVID-19, or to the adaptation to sociocultural diversity of the large city.

Manufacturing relatively inexpensive items in every area of engineering and science is the major focus of exploration resultant the world's contemporary economic setback. Making small-sized items that are inexpensive and lightweight while providing high quality is critical in today's and tomorrow's worlds. Nanotechnology has a significant role to play in this situation. Nano-objects or, in general, nanomaterials are especially preferred; nanotubes, especially those comprised of carbon, are one of the most popular types of nanostructures, and they are applied in a variety of chemical, biological and technical applications. This notion prompted us to investigate their many physical and chemical characteristics. We utilized topological descriptors to evaluate diverse nanotube structures such as armchair carbon and semi-capped nanotubes by using vertex-edge based indices to characterize distinct chemical structures via numerical quantitative analysis. Furthermore, we examined uncapped and semi-capped armchair carbon nanotubes and achieved adequate comparative findings.

An elderly female with metastatic adenocarcinoma of the lung and atrial fibrillation presented with multiple embolic strokes while on anticoagulation with Apixaban. After further investigation, a TEE showed lesions of non-bacterial thrombotic endocarditis on the mitral valve. A decision to switch the patient to LMWH for anticoagulation was then made and a follow-up TEE showed resolution of the NBTE. In this abstract, we show that heparin should remain as the anticoagulation agent of choice in the setting of NBTE associated with malignancy.

Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons. The mathematical study of chemicals are great interests of different specialties researchers. After transforming chemical structure into a graph, one can implement different theoretical and implicative study on structures. Mixed metric dimension is considered as one of the recent and most studied parameter of graph theory. In this concept, few suggested vertices are chosen such as all the vertices and edges of graph have unique locations or identifications. In this study, we discussed mixed metric parameter for the hollow coronoid structure.

The eigenvalues are significant in mathematics, but they are also relevant in other domains like as chemistry, economics, and a variety of others. In terms of our research, eigenvalues are used in chemistry to represent not only the form of energy but also the various physicochemical aspects of a chemical substance. We must comprehend the connection between mathematics and chemistry. The antibonding level is related to positive eigenvalues, the bonding level is associated to negative eigenvalues, and the nonbonding level is linked to zero eigenvalues. In this work, we studied some anticancer drug structures in terms of nullity, matching number, eigenvalues of adjacency matrix, and characteristics polynomials. As a result, Carmustine, Caulibugulone-E, Aspidostomide-E anticancer drug structures are stable, closed-shell molecules since their nullity is equal to zero.

For a simple connected graph $ G = (V, E) $, a vertex $ x\in V $ distinguishes two elements (vertices or edges) $ x_1\in V, y_1 \in E $ if $ d(x, x_1)\neq d(x, y_1). $ A subset $ Q_m\subset V $ is a mixed metric generator for $ G, $ if every two distinct elements (vertices or edges) of $ G $ are distinguished by some vertex of $ Q_m. $ The minimum cardinality of a mixed metric generator for $ G $ is called the mixed metric dimension and denoted by $ dim_m(G). $ In this paper, we investigate the mixed metric dimension for different families of ladder networks. Among these families, we consider Möbius ladder, hexagonal Möbius ladder, triangular Möbius ladder network and conclude that all these families have constant-metric, edge metric and mixed metric dimension.

In this study, bio-oil was produced from the pyrolysis of de-oiled karanja seed press cake in the presence of abandoned anthill as the catalyst. The anthill was characterised by SEM, EDX, XRF, XRD and surface area and pore size analysis. The pyrolysis experiments were carried out in an indigenously made furnace in a nitrogen atmosphere from 310 to 400 °C. The pyrolysis oil was collected at an optimised temperature and analysed through gas chromatography–mass spectrometry (GC-MS). The compounds identified via GC-MS of non-catalytic bio-oil were in the range of C5 to C19, and compounds identified from catalytic bio-oil were in the range of C2–C63. Furthermore, thermogravimetric analysis of the karanja seed press cake without and with anthill was carried out in a nitrogen atmosphere with temperature programme rates of 3, 12, 20 and 30 °C·min−1. Kinetic parameters were determined by applying the Kissinger equation. The activation energy (Ea) values for hemicelluloses, cellulose and lignin were obtained as 99.7 ± 0.4, 182.9 ± 0.5 and 199.5 ± 0.7 kJ·mol−1 without catalyst; and with catalyst, the Ea were lowered to 74.8 ± 0.2, 83.1 ± 0.4 and 108.0 ± 0.5 kJ·mol−1, respectively. From the results, it was concluded that the catalyst played a key role in lowering the activation energy for the pyrolysis reaction and enhanced the quality of the bio-oil obtained as well.

For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if $ x\in V(G) $ and $ \varphi(x) = \varphi_e(x) $ if $ x\in E(G) $, then $ k = \, \mbox{max}\, \{k_e, 2k_v\} $. The total $ k $-labeling $ \varphi $ is an edge irregular reflexive $ k $-labeling of $ G $ if every two different edges $ xy $ and $ x^\prime y^\prime $, the edge weights are distinct. The smallest value $ k $ for which such labeling exists is called a reflexive edge strength of $ G $. In this paper, we focus on the edge irregular reflexive labeling of antiprism, convex polytopes $ \mathcal D_{n} $, $ \mathcal R_{n} $, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work.

Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure. Motivated by the structure's applications and usage, we look into the edge-based metric parameters of this structure. In this draft, we have discussed edge metric dimension and their generalizations for the generalized perimantanes diamondoid structure and proved that each parameter depends on the copies of original or base perimantanes diamondoid structure and changes with the parameter λ or its number of copies.

The topological index of a graph gives its topological property that remains invariant up to graph automorphism. The topological indices which are based on the eccentricity of a chemical graph are molecular descriptors that remain constant in the whole molecular structure and therefore have a significant position in chemical graph theory. In recent years, various topological indices are intensively studied for a variety of graph structures. In this article, we will consider graph structures associated with zero-divisors of commutative rings, called zero-divisor graphs. We will compute the topological indices for a class of zero-divisor graphs of finite commutative rings that are based on their edge eccentricity. More precisely, we will compute the first and third index of Zagreb eccentricity, the eccentricity index of geometric arithmetic, the atomic bonding connectivity eccentricity index, and the eccentric harmonic index of the fourth type related to graphs constructed using zero-divisors of finite commutative rings $ \mathbb{Z}_{p^n}. $

The selective detection of ammonia (NH3), nitrogen dioxide (NO2), carbon oxides (CO2 and CO), acetone ((CH3)2CO), and toluene (C6H5CH3) is investigated by means of a gas sensor array based on polyaniline nanocomposites. The array composed by seven different conductive sensors with composite sensing layers are measured and analyzed using machine learning. Statistical tools, such as principal component analysis and linear discriminant analysis, are used as dimensionality reduction methods. Five different classification methods, namely k-nearest neighbors algorithm, support vector machine, random forest, decision tree classifier, and Gaussian process classification (GPC) are compared to evaluate the accuracy of target gas determination. We found the Gaussian process classification model trained on features extracted from the data by principal component analysis to be a highly accurate method reach to 99% of the classification of six different gases.

Indonesia, which consists of many tribes, religions, races, and languages, is a gift from God Almighty, for that it becomes a very urgent matter in maintaining and making relations among the nation's children into harmony and peace. Therefore, it needs mutual understanding and respect that differences do not have to be contradicted but must be a means of understanding each other to become a great nation. Educators need to understand that in the learning process. It is essential to manage and appreciate what is in the educational process, especially in cross-cultural social communication, so that no one is suspicious and suspicious of each other. It becomes absolute when cross-cultural social communication becomes the main of learning Islamic Religious Education in maintaining an inclusive, tolerant attitude in understanding and maintaining the wealth of our nation, namely the attitude of accepting differences which are a gift from God Almighty

Recent research on nanostructures proved their importance and implementation in various areas. In drug delivery systems, medicine and pharmaceutical, biological sensors, photodetectors, transistors, optical and electronic devices, in all these topics nanostructures are implemented directly or indirectly. Future advanced electronic devices are a motivation for the discovery of carbon nanotubes made Y-shaped junctions. Electronic switches, amplifiers, and three-terminal transistors are of great interest due to their interaction with Y-junctions. The concept of entropy determines the uncertainty of a system or network. Concepts of entropy are also commonly used in biology, chemistry, and applied mathematics. Entropy in the form of a graph can be classified into several types based on the requirements. Graph-based entropy was introduced in 1955. Edge-weighted-based entropy is one of the types of entropy. In this study, we look closely at the abstract form of Y-shaped junctions. For the generic view of Y-shaped junctions, we developed some edge-weight-based entropy formulas. On Y-shaped junctions, we discussed some edge-weighted and topological index-based concepts.

تُعتبر أنظمة ضخ المياه باستخدام الألواح الكهروضوئية من التطبيقات الواعدة والمهمة، حيث تساعد هذه الأنظمة في حماية البيئة والتقليل من انبعاثات غاز بالمقارنة مع الأنظمة التي تستخدم مولدات الديزل. يدرس هذا البحث استخدام نظام ضخ المياه الذي يعمل بالطاقة الكهروضوئية، ويظهر البحث الدراسات الفنية والاقتصادية والبيئية التي تقارن بين حلول الضخ الكهروضوئية والديزل. تبلغ تكلفة الـ لنظام الضخ الذي يعمل بالطاقة الكهروضوئية بينما تبلغ تكلفة لنظام الضخ الذي يعمل بالديزل .

Abstract Background Coronavirus disease 2019 (COVID-19) caused by the novel coronavirus-infected millions globally. Despite a wide range of advised options for the treatment of COVID-19, a single strategy to tackle this pandemic remains elusive, thus far. That is why we are conducting a clinical trial to find out the efficacy of iodine complex to clear a viral load of severe respiratory syndrome coronavirus-2 (SARS-CoV-2) along with a reduction in time taken to alleviate symptoms. Method The proposed study is a placebo-controlled, add-on, randomized trial using parallel group designs. This is a closed-label and adaptive with sample size reassessment, multi-centered design with a 1:1:1:1 allocation ratio and superiority framework. It will be conducted in Shaikh Zayed Post-Graduate Medical Complex, Ali Clinic, and Doctors Lounge, Lahore, Pakistan. This study will have three arms of mild to moderately symptomatic COVID-19 patients (50 patients in each) which will receive ionic-iodine polymer complex with 200 mg of elemental iodine: interventional arm A will have encapsulated, arm B will receive suspension syrup form, arm C will get throat spray, while arm X will be standard care with placebo. Data will be collected on self-constructed, close-ended questionnaires after obtaining written consent. Data will be analyzed using SAS version 9.4. COVID-19 patients will be monitored by RT-PCR and HRCT (high-resolution computed tomography) chest. In addition to these, the duration of the symptomatic phase and mortality benefits will be analyzed in both groups. Discussion The study is designed to measure the superior efficacy of the iodine complex as an add-on in treating COVID-19-positive patients with mild to moderate symptoms. This combination is hypothesized to improve various parameters like rapid viral load reduction, clinical and radiological improvement, lower mortality, and reduction in hospitalization. The trial will aid in devising a better strategy to cope with COVID-19 in a relatively inexpensive and accessible way. The implications are global, and this could prove itself to be the most manageable intervention against COVID-19 especially for patients from limited-resource countries with deprived socioeconomic status. Trial registration ClinicalTrials.gov NCT04473261 . Registered on July 16, 2020.

In this paper, we determine the exact metric and fault-tolerant metric dimension of the benzenoid tripod structure. We also computed the generalized version of this parameter and proved that all the parameters are constant. Resolving set L is an ordered subset of nodes of a graph C, in which each vertex of C is distinctively determined by its distance vector to the nodes in L. The cardinality of a minimum resolving set is called the metric dimension of C. A resolving set Lf of C is fault-tolerant if Lf∖b is also a resolving set, for every b in Lf. Resolving set allows to obtain a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represents the atom and bond types, respectively.

Due to its superlative physical qualities and its beauty, the diamond is a renowned structure. While the green-colored perimantanes diamondoid is one of a higher diamond structure. Motivated by the structure’s applications and usage, we look into the metric-based parameters of this structure. In this draft, we have discussed metric dimension and their generalizations for the generalized perimantanes diamondoid structure and proved that each parameter depends on the copies of original or base perimantanes diamondoid structure and changes with the parameter ${n}$ or its number of copies.

Background and Objective: Microbial fuel cell (MFC) is a new green technology that uses the catabolic ability of microorganisms to produce bioenergy while simultaneously removing organic matter and other wastewater contaminants. Electrode material is one of the factors affecting the performance of microbial fuel cells. The aim of this study was to investigate the performance of microbial fuel cells in COD removal and bioenergy production from synthetic and real beverage wastewater. Materials and Methods: In this research, a two-chamber microbial fuel cell with Nafion membrane and aerated cathode was set up using two electrodes made of carbon felt and flat graphite after being contacted by synthetic wastewater with a concentration of COD 5000 mg/L and real beverage wastewater. Organic matter removal efficiency and voltage, power density and maximum current were determine. Results: Experimental results showed that maximum COD removal efficiency of 92 % was achieved in synthetic wastewater and with a carbon felts electrode. In this condition, maximum voltage, power density and output current density of 469 mV, 175.28 mW/m2, and 855 mA/m2, were obtained, respectively. However, by using real industrial wastewater (beverage), maximum removal efficiency of COD, voltage, power density and output current density, related to carbon felt electrodes ‎were obtaines as 84 %, ‎460 mV, 91/65 mW/m2, and 635 mA/m2, respectively. Conclusion: The findings showed that synthetic wastewater outperforms microbial fuel cells in terms of bioelectric production and organic matter removal as compared to real wastewater (beverage). The reason for the decrease in the cell performance might be the presence of solids and other confounding pollutants in real wastewater.

The analgesic efficacy of the gabapentin-tramadol combination was compared with meloxicam-tramadol and tramadol perioperative analgesic regimens in cats brought to the clinic for ovariohysterectomy. Thirty adult cats belonging to comparable demographics (age, body weight), were enrolled into a randomized, blinded study after due consent from their owners into four treatment groups. A Gabapentin-Tramadol group (GT-group, n = 10), Meloxicam-Tramadol group (MT-group, n = 10), and a Tramadol group (T-group, n = 10) were formed. Gabapentin capsules at 50 mg were administered orally 2 hours before surgery while the rest received a placebo dose. Tramadol (2 mg/kg, IM) and meloxicam at (0.2 mg/kg, SC) were injected immediately prior to anesthetic premedication. Anesthetic protocol involved premedication with ketamine and xylazine, while anesthesia was induced using propofol. Inhalant isoflurane anesthesia was used to maintain a surgical plane. GT group scored lower on IVAS as well as CPS than MT group, and T group for up to 8 hours after surgery. The mechanical nociceptive threshold remained higher (98±0) for up to 12 hours postoperatively a nd serum cortisol concentrations remained significantly lower during the 24hr period. The addition of gabapentin to the tramadol regimen significantly improved analgesia and mechanical nociceptive threshold than when used on its own.

Abstract Aims Cardiac allograft vasculopathy (CAV) is the major cause of increased morbidity and mortality after heart transplantation. Peripheral endothelial dysfunction (PED) is associated with early atherosclerosis and future risk of major adverse cardiovascular events (MACE) in non‐heart transplant population. We aimed to investigate the association of PED with future MACE, and plaque progression assessed by intravascular ultrasound (IVUS) after heart transplantation. Methods and results We included 66 transplant patients who underwent serial IVUS surveillance for CAV and baseline assessment of peripheral endothelial function using reactive hyperaemia peripheral arterial tonometry. PED was defined as reactive hyperaemia index

Many studies indicate the importance of including the instructional illustrations (pictures, drawings, concrete objects …etc.) in childhood education learning materials and employing them in a way that suits the psychological and cognitive levels of young children. In this context, the current study aimed to develop a list of standards to be considered and adopted in designing instructional illustrations, and to reveal the perceptions of childhood teachers about the extent to which these standards are considered in instructional illustrations used in children's learning materials. The participants were childhood education teachers in the Jordanian region of Irbid, who were randomly selected. Two hundred thirty-four teachers completed the questionnaire online. The scale consisted of a total of 34 items distributed over four dimensions. The results showed that the scores of teachers' estimation about employing design standards in the instructional illustrations used in childhood education came at low levels, ranging from average to low, and did not reach high ratings. The study also revealed that there is an impact attributed to teaching experience on teachers' perceptions about the extent to which these standards are employed in instructional illustrations, while there is no impact of gender, academic qualification, or the classes taught by the teachers.

This study examines the use of five tashbīh (simile) particles which appear in close frequency in pre-and early Islamic poetry and in the Qurʾan. The particles are ka-(as), ka-mā (such as), mithl (like), and derivatives of the roots ḥsb (deem) and shbh (looks like, similar to). As well as understanding classical Arabic techniques for composition of similes, the study examines aspects of the interrelationship between the Qurʾan and the poetry corpus, the single surviving Arabic text to which the scripture was exposed. It finds greater common structural and lexical similarities between poetry and the Qurʾan in its earlier period (during the Meccan Revelation, 610–622 CE) than later, following the migration of Prophet Muḥammad to Medina (622–632 CE), when other ways of using these particles developed. This suggests surveying these techniques in other texts possibly known to Medinian society, such as the Bible. The present study outlines the premise that qurʾanic composition moved from the influence of the Arabic prototype seen in the poetry in the earliest periods of Revelation to a different form in later periods (texts, possibly biblical). This premise can be further explored by future examination of the interrelationship between the Qurʾan, pre- and early Islamic poetry and the Bible.

Objective: To determine the diagnostic accuracy of cord blood bilirubin in predicting neonatal hyperbilirubinemia, taking neonatal hyperbilirubinemia within one week of birth as the gold standard. Study Design: Across-sectional study. Place and Duration of Study: The Study was conducted at the Department of Pediatric Medicine, Sheikh Zayed Hospital, Rahim Yar Khan, Pakistan from 7 September 2020 to 6 March 2021. Methods: A total of 366 term neonates of both gendersgenders were included. Neonates with congenital hypothyroidism, neonatal hepatitis, biliary atresia, and sepsis were excluded. After getting informed consent from parents, a cord blood sample was taken and sent to the institutional laboratory for measuring total bilirubin levels, and neonatal hyperbilirubinemia (yes/no) was noted. All neonates were followed by the researcher for one week and neonatal hyperbilirubinemia was noted. Results: The study yielded 193 true positive and 14 false positive cases, along with 7 false negative and 152 true negative cases, with a statistically significant p-value of 0.0001. Overall, the diagnostic accuracy of cord blood bilirubin in predicting neonatal hyperbilirubinemia, using neonatal hyperbilirubinemia within one week of birth as the gold standard, was found to be 96.50% for sensitivity, 91.57% for specificity, 93.24% for positive predictive value, 95.60% for negative predictive value, and 94.26% for diagnostic accuracy. Conclusion: This study has shown that cord blood bilirubin has a rather good diagnostic accuracy for predicting newborn hyperbilirubinemia. How to cite this: Majeed M, Ahmed D, Hanif D, Khaliq H, Ahmad A, Khan ZA. Diagnostic Accuracy of Cord Blood Bilirubin in Predicting Neonatal Hyperbilirubinemia, Taking Neonatal Hyperbilirubinemia within One Week of Birth as Gold Standard. Life and Science. 2023; 4(4): 401-409. doi: http://doi.org/10.37185/LnS.1.1.347

Salicylic acid (SA) is mainly associated with the regulation of plant growth particularly in salinity stress conditions and this signaling molecule exists in pivotal parts of plant. The objective of this research analysis was to overcome stress condition by distinct foliar treatments of Salicylic acid, for instance, 0 and 100 mM. Foliar applications of SA on maize were rendered on 10 days later than transplanting under a hydroponics experiment. Plants were grown under non-saline (S0= 0 mM NaCl) and saline (S1= 100 mM NaCl) conditions. Evaluation of biochemical, physiological and morphological attributes of maize was rendered after harvesting of plants. The experimental layout of Completely Randomized Design (CRD) under a factorial arrangement with three replications of each treatment was assigned for this study. According to our results it was confirmed that cultivation of maize under saline condition reduced the morphological, physiological and biochemical attributes of plant. However, exogenous application of SA on maize had a positive impact on the above mentioned traits under presence and absence of saline environment. Finally, it was justified that exogenous application of variable concentration of SA significantly improves whole parameters of maize cultivar.

Network theory gives an approach to show huge and complex frameworks through a complete arrangement of logical devices. A network is made is made of vertices and edges, where the degree of a vertex refers to the number of joined edges. The degree appropriation of a network represents the likelihood of every vertex having a particular degree and shows significant worldwide network properties. Network theory has applications in many disciplines like basic sciences, computer science, engineering, medical, business, public health and sociology. There are some important networks like logistical networks, gene regulatory networks, metabolic networks, social networks, derived networks. Topological index is a numerical number assigned to the molecular structure/netwrok which is used for correlation analysis in physical, theoretical and environmental chemistry. The hex-derived networks are created by hexagonal networks of dimension t, these networks have an assortment of valuable applications in computer science, medical science and engineering. In this paper we discuss the reverse degree-based topological for third type of hex-derived networks.

Introduction The long-term historical process that has led to the emergence of a new Western civilization and is today called modernity, has exposed all aspects of human life to change and revision, including the change of social structures and the transformation of the values ​​that govern these structures. One of the most important challenges in entering the modern world in the field of social structures and values ​​that have emerged from the beginning of this historical process and has gone through many ups and downs, regardless of the many conflicts that can be raised in many ways has been the subject of criticism of the patriarchal view that governs the structure and social values ​​of the traditional world and the demand for equal rights for men and women. After the acquaintance of oriental nations with Western modernity and under the influence of Western social developments, this demand was gradually formed among some intellectuals in Islamic and Asian countries, especially educated women and intellectuals, who were mainly poets and writers and led to the emergence of women's writing, including poetry and prose in the literature of these countries. Feminine writing has several components, one of which is the critique of various aspects of the patriarchal social system. Based on what has been mentioned, due to the many commonalities and similarities in cultural, historical and social fields and roots between the Iranian and Pakistani communities, including the traditional and religious interests and contexts along with the social movement towards development and modernity, It seems that women's poetry in Iran and Pakistan, despite slight differences, has many similarities in terms of reflecting women's issues and problems, as well as common feminine feelings and experiences. Therefore, this research tries to compare and analyze the issue of the critique of the patriarchal social system in the works of Simin Behbahani and Fahmida Riaz, two contemporary Iranian and Pakistani female poets, using a comparative approach. Accordingly, the present study is a report of methodical and scientific efforts in order to find answers to the following questions: - How is the critique of the patriarchal social system seen in the poetry of Fahmida Riaz and Simin Behbahani? - How can the similarities and differences of the critique of the patriarchal social system in the poetry of the two selected poets be analyzed? Methodology This is theoretical research based on written documents and sources, conducted in a descriptive-analytical method and with the approach of sociology of literature has studied the critique of the patriarchal social system in a comparative way in the poetry of Simin Behbahani and Fahmida Riaz. 3.Discussion In a patriarchal society, a man is a first-class citizen and a woman a second-class one. The context, time, and society in which Simin Behbahani and Fahmida Riaz live are also patriarchal societies, which due to gender discrimination in the social and value system, not only dismiss a large portion of women's inalienable rights, but also they unintentionally and unjustly impose many problems and difficulties on them. In the following sections, the researchers will review and analyze some of these issues that are reflected in the works of these two Iranian and Pakistani poets. Simin Behbehani In a patriarchal social structure which is based on the superiority of the male sex, women lack originality and are merely a means of meeting the needs of the superior sex, i.e., women are the means of sexual satisfaction for men. For this reason, in women's writings, this instrumentalistic view of women, which is the result of a patriarchal social structure, is always criticized. Simin Behbahani tells the story of a man who sees a woman merely as a sexual commodity in the poem "Vasteh". Besides this poem, Behbahani in another poem called "The Dancer" narrates the lust of men in a seemingly open society, whose leaders are in the pursuit of modernization and call it the gate of their civilization. Behbahani believes that in a patriarchal society, all forms of freedom have been taken away from women in the name of tradition or under the pretext of modernity. Just as the dancer is trapped in the circle of men's asceticism in the name of freedom and the housewife is also forced to stay home and avoid socialization. In the poem "Zan dar Zindan-e Tala" (Woman in the Gold Prison), Simin complains about the forced residence of the contemporary Iranian woman in the gold palace, without authority, freedom and independence. Other issues that provoke Simin Behbahani's social critique are polygamy and the right of men to divorce, along with various manifestations of male violence and its social consequences, such as, sexual and physical violence, abandonment of children and evasion of responsibility towards the family, as well as forcing girls into marriage, and above all, confronting women not from the perspective of the human element but as a means of men’s satisfaction and reproduction are the most important social problems of women in the patriarchal society of Iran, which are usually depicted in the form of often long poems, with a large number of verses and in a narrative tone and atmosphere. Poems that include such themes in Simin Behbahani’s collection of works, include poems such as Fe’l-e Majhool (The Passive verb), Ilkhan Sitareh-ha (the Ilkhan of the stars), Jibb Bor (the pickpocket), Dard-e Niaz (the pain of need), Anja wa Eenja (here and there), Khoon-e Sabz (green blood), Zarkhrid (Bought), etc., in general her poetic works, such as Jay-e pa (Footprint, 1954), Chelcheragh (Chandelier, 1955), Marmar (Marble, 1961), Rastakhiz (Resurrection, 1971), Khati ze Sor’at va Atash (A Line of Speed and Fire,1980), Dasht-e Arzhan (The Plain of Arzan,1983), Kaghazin Jameh (Paper-Thin Vestment, 1989), Yek Daricheh-e Azadi (A Window to Freedom, 1995) and Tazeh-ha (The Latest, 2008) are scattered. Although the origins of Behbahani's critique of the patriarchal social system and the patriarchal values that govern Iranian society can be attributed to the feminist ideas, but certainly, this feminism is by no means anti-male and extremist and has a perfectly rational, moderate and balanced basis. Fahmida Riaz Fahmida Riaz is also one of the poets who has paid attention to the issues and problems arising from the patriarchal social system for Pakistani women, and this issue is one of the central discourses in the works and especially the poems of this famous Pakistani poet. Fahmida Riaz was born on July 28, 1946, in the city of Meerut. Fahmida grew up in Hyderabad (Pakistan) and her father died when she was 4 years old. During her school years (1960), she composed her first poem and published it in "Fonoon" magazine (Mari, 2004, pp. 14-15). Fahmida got married in 1965, and after marriage, she went to England and published the book Badan Darideh (The Torn Body) (1973) there. She returned to Pakistan a few years later from the United Kingdom and served for some time as the chairman of the National Book Council in Islamabad. When General Zia-ul-Haq came to power, he realized that she was the director of the literary magazine "Avaz". The military government did not come to terms with her and she went to India for several years and did not return until General Zia-ul-Haq was alive (Shams ul-Haqq, 2008, p. 381). Fahmida Riaz, in addition to being a poet, was also a prose writer and translator, and some of her prose works include Karachi, Goodwari, Tem Kabir, Zindeh Bahar, etc. Fahmida Riaz's translations are often from the masterpieces of the world poetry in Urdu (poetry and prose), one of which is Kohli Darichi si (from the open window), a translation of selected poems by Forough Farrokhzad, an Iranian Persian poet. In essence, this expresses the poet's belonging and her acquaintance with the living and dynamic corpus of contemporary Persian poetry (Riaz, 1998, pp. 2-3). She has another book called Ye Khaneh Ab va Gel (This House of Water and Mud), which is a poetic translation of selected lyric poems of Divan Shams-e Tabrizi and indicates his familiarity with classical Iranian literature (Rumi, 2006, pp. 1-2). Shadiani is a story that has been translated into Urdu prose by Fahmida Riaz and this Novel is from the Egyptian Najib Mahfouz who won a Nobel Prize (Mahfouz, 2000, p. 2). Apart from these, she wrote stories such as Qaleh Framosh, Adhora Adami, Halqa meri Zanjir ka, Apna Jurm Sabit hey etc. Fahmida Riaz died on November 21, 2018. Although Riaz has made a critique of the patriarchal social system in the context of the tradition of its prestige, she has not neglected the imposition of new problems on women, such as freedom. These problems, which sometimes occur in Eastern societies, are doubly severe in political regimes with a capitalist approach, like the United States or France, which is seen as the origin of democracy (Sarvarian, 2004, p. 302). Denying the physical and mental abilities of women and limiting their social function to physical characteristics is one of the topics of concern for Riaz and the poem "The Beauty Contest" is a strong protest against the behaviour in which the female body has become the subject of writers, poets and artists. This poem is about beautiful girls who participate in the beauty contest and there, just by appearance and physical criteria, a worthy girl is selected from the point of view of men. The poem "Chador and Chardivari" is one of the most important poems of Riaz regarding women's issues in the patriarchal social system, which has addressed various issues in this regard. Part of this poem depicts the oppression of men and their cruel domination over women who have been exploited and sometimes sexually abused for low wages. Fahmida Riaz describes the captivity of women in the poem "smile of a woman" and so it challenges the idols of the new temple, which are international symbols and demands peace from them. The poem "Chador and Chahardivari" tells the story of a woman who is forced to wear a hijab to cover herself. But the woman, who is a symbol of the poet herself, cleverly points to more important social priorities and points out the poverty of the society to the rulers. And ironically, he asks them to first bury the shrouded dead who have been left on the ground by the pressure of poverty. In another layer of this poem, the corpse can be considered a symbol of women who in the house of fanatical men have the status of the moving dead who need to be covered more than others. Other issues such as polygamy of men, types of verbal, physical and psychological violence, forced marriage and social inequalities are other social problems of women in Pakistani society that Fahmida Riaz in its poetic works, like Pathar ki Zaban (Stone Language, 1967), Badan Daridah (the Torn Body, 1973), Dohup (Sunshine, 1976), Kia Tum Pura Chand Na Dikhu Gay (Will You Not See the Full Moon, 1984), Hamarkab (Travel companion, 1988), Admi ki Zindigi (Human Life, 1999), Kulyat-e Fahmida Riaz Sab Lal o Gowhar (Generalities of Riaz called Sab Lal and Gowhar, 2011) have been criticized. 4.Conclusion The results of the present study on the critique of the patriarchal social system in the poetry of Simin Behbahani and Fahmida Riaz are as follows: - One of the important topics and discourses in the poetry of Simin Behbahani and Fahmida Riaz is the critique of the patriarchal social system and the moral and social values ​​that govern it and the confrontation with the violation of some social rights of women in Iranian and Pakistani society; - Due to cultural, historical, religious, social, etc. commonalities that exist between Iran and Pakistan ​- topics related to the subject of this research were often in common in the works of both poets and were often expressed in a common style (narrative style); - Although Fahmida Riaz is known as one of the activists of the women's social movement in Pakistan, neither of the two mentioned poets - based on their poetic works - can be considered a feminist poet in its radical and even liberal sense, because the criticisms expressed in their poetry are completely humane and respectful of men while recognizing their rights and they are sometimes accompanied by a critique of the values ​​that govern the liberal-democratic discourse of the New World. - Simin Behbahani's social criticisms are more superficial, emotional and soft, but Fahmida Riaz's critiques are deep, thoughtful, sharp and reckless, with political connotations and critiques of the ruling power; - Despite the many thematic similarities in the critique of the patriarchal social system in the works of the two selected poets, the influence of Fahmida Riaz on Simin Behbahani seems very unlikely. But, Fahmida Riaz's influence from Simin Behbahani, due to her fluency in Persian language, complete familiarity with classical Persian poetry and interest in contemporary Iranian poetry, as seen in the introduction of her translations of Shams lyric poems and Forough Farrokhzad's poems in Urdu, is quite probable.

Natural zeolites are frequently referred to as macromolecular sieves. Because of relatively inexpensive cost of installation, zeolites networks are highly trendy chemical networks. Amongst the most researched types of zeolite networks is the sodalite network. It contributes to the elimination of greenhouse gases. To investigate the above widely tested, we employ an authentic mathematical tool known as topological descriptors or index, which displays some physical and chemical properties numerically. To fully comprehend the structure, we compare different legitimate properties via topological indices, concluding in the form of figurative comparisons. In particularly, we measure some reverse degree-based indices for the sodalite materials network and put some light on the behavior of this network, in the form of topological descriptors and numerically designed equation of such network. This research is novel in terms of no one studied reverse-degree-based topological indices for this chosen structure.

Let G = (V(G), E(G)) be a graph with no loops, numerous edges, and only one component, which is made up of the vertex set V(G) and the edge set E(G). The distance d(u, v) between two vertices u, v that belong to the vertex set of H is the shortest path between them. A k-ordered partition of vertices is defined as β = {β1, β2, …, βk}. If all distances d(v, βk) are finite for all vertices v ∈ V, then the k-tuple (d(v, β1), d(v, β2), …, d(v, βk)) represents vertex v in terms of β, and is represented by r(v|β). If every vertex has a different presentation, the k-partition β is a resolving partition. The partition dimension of G, indicated by pd(G), is the minimal k for which there is a resolving k-partition of V(G). The partition dimension of Toeplitz graphs formed by two and three generators is constant, as shown in the following paper. The resolving set allows obtaining a unique representation for computer structures. In particular, they are used in pharmaceutical research for discovering patterns common to a variety of drugs. The above definitions are based on the hypothesis of chemical graph theory and it is a customary depiction of chemical compounds in form of graph structures, where the node and edge represent the atom and bond types, respectively.