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Drug-drug interaction (DDI) prediction aims to predict and evaluate potential interactions between different drugs, assisting healthcare professionals in optimizing drug therapy, enhancing treatment outcomes, and minimizing adverse effects from drug combinations. Traditional research has extensively focused on whether two drugs interact, but predicting the specific events or effects resulting from these interactions may be more effective in understanding the underlying mechanisms of drug combinations. However, data scarcity in drug research significantly hampers the effectiveness of computational models. To address these challenges, we propose FSRM-DDIE, a novel few-shot drug-drug interaction events (DDIE) prediction model. This metric-based meta-learning framework first learns the features of a DDIE using a feature extractor fusing a graph neural network and an auto-encoder Siamese network. Subsequently, a relation metrics module is proposed to capture similar relations between events for classification. By employing meta-learning, our model could perform effectively even with fewer and rare events. Through the comparative experiments, FSRM-DDIE outperforms state-of-the-art methods, demonstrating its potential for accurately predicting DDIE and providing options for understanding drug-drug interactions despite data limitations. In addition, we discuss limitations of the methodology and possible future research trends. [ABSTRACT FROM AUTHOR]

A k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set. The k-total domination number γ k t (G) is the cardinality of the smallest k-total dominating set. For k = 1 , 2 , the k-total dominating number is called the total and the double total dominating number, respectively. In this paper, we determine the exact values for the total domination number on a linear and on a double octagonal chain and an upper bound for the total domination number on a triple octagonal chain. Furthermore, we determine the exact values for the double total domination number on a linear and on a double octagonal chain and an upper bound for the double total domination number on a triple octagonal chain and on an octagonal grid O m , n , m ≥ 3 , n ≥ 3 . As each vertex in the octagonal system is either of degree two or of degree three, there is no k-total domination for k ≥ 3 . [ABSTRACT FROM AUTHOR]

The development of new drugs is a vital effort that has the potential to improve human health, well-being and life expectancy. Molecular property prediction is a crucial step in drug discovery, as it helps to identify potential therapeutic compounds. However, experimental methods for drug development can often be time-consuming and resource-intensive, with a low probability of success. To address such limitations, deep learning (DL) methods have emerged as a viable alternative due to their ability to identify high-discriminating patterns in molecular data. In particular, graph neural networks (GNNs) operate on graph-structured data to identify promising drug candidates with desirable molecular properties. These methods represent molecules as a set of node (atoms) and edge (chemical bonds) features to aggregate local information for molecular graph representation learning. Despite the availability of several GNN frameworks, each approach has its own shortcomings. Although, some GNNs may excel in certain tasks, they may not perform as well in others. In this work, we propose a hybrid approach that incorporates different graph-based methods to combine their strengths and mitigate their limitations to accurately predict molecular properties. The proposed approach consists in a multi-layered hybrid GNN architecture that integrates multiple GNN frameworks to compute graph embeddings for molecular property prediction. Furthermore, we conduct extensive experiments on multiple benchmark datasets to demonstrate that our hybrid approach significantly outperforms the state-of-the-art graph-based models. The data and code scripts to reproduce the results are available in the repository, https://github.com/pedro-quesado/HybridGNN. [ABSTRACT FROM AUTHOR]

Accurate predictions of molecular properties are crucial for advancements in drug discovery and materials science. However, this task is complex and requires effective representations of molecular structures. Recently, Graph Neural Networks (GNNs) have emerged as powerful tools for this purpose, demonstrating significant potential in modeling molecular data. Despite advancements in GNN predictive performance, existing methods lack clarity on how architectural choices, particularly activation functions, affect training dynamics and inference stages in interpreting the predicted results. To address this gap, this paper introduces a novel activation function called the Sine Linear Unit (SLU), aimed at enhancing the predictive capabilities of GNNs in the context of molecular property prediction. To demonstrate the effectiveness of SLU within GNN architecture, we conduct experiments on diverse molecular datasets encompassing various regression and classification tasks. Our findings indicate that SLU consistently outperforms traditional activation functions on hydration free energy (FreeSolv), inhibitory binding of human β secretase (BACE), and blood brain barrier penetration (BBBP), achieving the superior performance in each task, with one exception on the GCN model using the QM9 data set. These results underscore SLU's potential to significantly improve prediction accuracy, making it a valuable addition to the field of molecular modeling. [ABSTRACT FROM AUTHOR]

Nanostructures are tiny objects at the molecular and microscopic scale, with carbon nanotubes being the most notable among them. The elements possess exceptional microelectronic properties and other unique characteristics. Researchers have recently focused on the mathematical features of these materials. Molecular descriptors are crucial in mathematical chemistry, particularly in QSAR and QSPR modeling. Topological indices hold a significant position among them. This study presents the precise formulation of the ten most crucial topological indices for a benzene ring positioned on a P-type surface within the highly symmetric 2D lattice BCZ 48 . We have incorporated the computed indices to develop a predictive model for the graph energy of the 2D lattice and, in addition, provided the NMR patterns and the HOMO-LUMO gap. [ABSTRACT FROM AUTHOR]

Abstract Nanostructures are tiny objects at the molecular and microscopic scale, with carbon nanotubes being the most notable among them. The elements possess exceptional microelectronic properties and other unique characteristics. Researchers have recently focused on the mathematical features of these materials. Molecular descriptors are crucial in mathematical chemistry, particularly in QSAR and QSPR modeling. Topological indices hold a significant position among them. This study presents the precise formulation of the ten most crucial topological indices for a benzene ring positioned on a P-type surface within the highly symmetric 2D lattice $$\hbox {BCZ}_{48}$$ BCZ 48 . We have incorporated the computed indices to develop a predictive model for the graph energy of the 2D lattice and, in addition, provided the NMR patterns and the HOMO-LUMO gap.

Abstract This work initiates a concept of reduced reverse degree based $$\mathcal {RR_D\,M}$$ RR D M -Polynomial for a graph, and differential and integral operators by using this $$\mathcal {RR_D\,M}$$ RR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the $$\mathcal {RR_D\,M}$$ RR D M -Polynomial. The topological descriptors, denoted as $$\mathbb{T}\mathbb{D}$$ T D ’s, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

The purpose of this paper is to discuss the use of topological indices (TIs) to anticipate the physical and biological aspects of innovative drugs used in the treatment of Alzheimer's disease. Degree-based topological indices are generated using edge partitioning to assess the drugs Tacrine, Donepezil, Ravistigmine, Butein, Licochalcone-A and Flavokqwain-A. Furthermore, using linear regression, a quantitative structure–property relationship (QSPR) model is developed to predict the characteristics such as boiling point (BP), flash point (FP), molar volume (MV), molecular weight, complexity and polarizability. The findings show that topological indices have the potential to be used as a tool for drugs discovery and design in the field of Alzheimer's disease treatment. [ABSTRACT FROM AUTHOR]

This work initiates a concept of reduced reverse degree based RR D M -Polynomial for a graph, and differential and integral operators by using this RR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the RR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study. [ABSTRACT FROM AUTHOR]

The structures of fentanyl and its analogues are easy to be modified and few types have been included in database so far, which allow criminals to avoid the supervision of relevant departments. This paper introduces a molecular graph-based transformer model, which is combined with a data augmentation method based on substructure replacement to generate novel fentanyl analogues. 140,000 molecules were generated, and after a set of screening, 36,799 potential fentanyl analogues were finally obtained. We calculated the molecular properties of 36,799 potential fentanyl analogues. The results showed that the model could learn some properties of original fentanyl molecules. We compared the generated molecules from transformer model and data augmentation method based on substructure replacement with those generated by the other two molecular generation models based on deep learning, and found that the model in this paper can generate more novel potential fentanyl analogues. Finally, the findings of the paper indicate that transformer model based on molecular graph helps us explore the structure of potential fentanyl molecules as well as understand distribution of original molecules of fentanyl. [ABSTRACT FROM AUTHOR]

The most important application of anticancer drugs in various forms (alkylating agents, hormones agents, and antimetabolites) is the treatment of malignant diseases. Topological indices are widely used in the field of chemical and medical sciences, especially in studying the chemical, biological, clinical, and therapeutic aspects of drugs. In this article, the temperature indices in anticancer drugs molecular graphs such as Carmustine, Convolutamine F, Raloxifene, Tambjamine K, and Pterocellin B were calculated and then analyzed based on physical and chemical properties. The analysis was performed by identifying the best regression models based on temperature indices for six physical and chemical features of anticancer drugs. The results indicated that temperature indices were essential topological indices that predict the properties of anticancer drugs, such as boiling point, flash point, enthalpy, molar refractivity, molar volume, and polarizability. It was also observed that the r value of the regression model was more than 0.6, and the p value was less than 0.05. [ABSTRACT FROM AUTHOR]

Silicon carbide is a captivating semiconductor material for electrical and electro-optical applications requiring high temperatures. Silicon carbide is a crucial non-oxide ceramic with a wide range of uses in manufacturing. It has special properties like high rigidity and durability, heat and chemical constancy, a high melting point, oxidation resistance, powerful erosion resistance, etc. Due to all of these properties, silicon carbide is the perfect material for high-power, high-temperature electrical devices as well as erosion and cutting purposes. Silicon carbide materials are frequently used in different fields of nuclear materials and semiconductor materials because of their outstanding radiation resistance, thermal conductivity, oxidation resistance, and mechanical strength. This study presents various K-Banhatti entropies, redefines Zagreb entropies, and the atom-bond sum connectivity entropy of the double and strong double graphs of silicon carbide [ S i 2 C 3 - I (r , s) ], and presents a numerical and graphical analysis of these results. The QSPR analysis of silicon carbide is performed for four characteristics Poisson's ratio, shear modulus, Young's modulus and bulk modulus through linear and quadratic regression analysis and found the best prediction. These models provide scientists with a new way of estimating physicochemical properties. [ABSTRACT FROM AUTHOR]

Skin cancer poses a significant risk to the healthcare system worldwide and is projected to increase substantially over the next two decades, particularly if not detected in its early stages. The primary aim of this study is to construct a quantitative structure-property relationship (QSPR) by correlating calculated entropies with topological indices and specific physical-chemical properties of pharmaceuticals, in order to enhance their usefulness. The bicubic regression model is constructed through degree-based topological entropies to perform the QSPR analysis for the prediction of physiochemical properties like polar surface area, complexity, molar refractivity, boiling point, and polarity of skin cancer drugs. It is also examined that degree-based entropies provide best-fit models for skin cancer physiochemical properties. We inspected five physio-chemical properties of these anticancer drugs and found this methodology suitable for predicting best-fit approximations regarding R2 value. It is expected that this approach will be very favourable to examining problems related to mathematical chemistry.

Abstract Accurate structure elucidation of biologically active molecules is crucial for designing and developing new drugs, as well as for analyzing their pharmacological activity. In this study, density functional theory calculations are applied to explore the electronic structure and properties of phenethylamine derivatives, including Amphetamine, Methamphetamine, and Methylene Dioxy Methamphetamine(MDMA). The investigation encompasses various aspects such as geometry optimization, vibrational analysis, electronic properties, Molecular Electrostatic Potential analysis, and local and global descriptor analysis. Additionally, the study utilizes Natural Bond Orbital analysis and Quantum Theory of Atoms in Molecules to investigate the chemical bonding and charge density distributions of these compounds. Experimental techniques such as Fourier transform infrared (FT-IR) and Raman spectroscopic analysis are employed in the range of 4000-400 $$cm^{-1}$$ c m - 1 and 4000-50 $$cm^{-1}$$ c m - 1 , respectively. Theoretical vibrational analysis with Potential Energy Distribution(PED) assignments is conducted, and the resulting frequencies are compared to experimental spectral data, revealing good agreement. By correlating various structural parameters with the pharmacological activity of each derivative, computational structure elucidation aids in understanding the unique actions of phenethylamine derivatives. The obtained results offer a comprehensive understanding of the molecular behavior and properties of these drugs, facilitating the development of new drugs and therapies for addiction and related disorders.

Accurate structure elucidation of biologically active molecules is crucial for designing and developing new drugs, as well as for analyzing their pharmacological activity. In this study, density functional theory calculations are applied to explore the electronic structure and properties of phenethylamine derivatives, including Amphetamine, Methamphetamine, and Methylene Dioxy Methamphetamine(MDMA). The investigation encompasses various aspects such as geometry optimization, vibrational analysis, electronic properties, Molecular Electrostatic Potential analysis, and local and global descriptor analysis. Additionally, the study utilizes Natural Bond Orbital analysis and Quantum Theory of Atoms in Molecules to investigate the chemical bonding and charge density distributions of these compounds. Experimental techniques such as Fourier transform infrared (FT-IR) and Raman spectroscopic analysis are employed in the range of 4000-400 c m - 1 and 4000-50 c m - 1 , respectively. Theoretical vibrational analysis with Potential Energy Distribution(PED) assignments is conducted, and the resulting frequencies are compared to experimental spectral data, revealing good agreement. By correlating various structural parameters with the pharmacological activity of each derivative, computational structure elucidation aids in understanding the unique actions of phenethylamine derivatives. The obtained results offer a comprehensive understanding of the molecular behavior and properties of these drugs, facilitating the development of new drugs and therapies for addiction and related disorders. [ABSTRACT FROM AUTHOR]

Accurately predicting Drug-Drug Interaction (DDI) is a critical and challenging aspect of the drug discovery process, particularly in preventing adverse reactions in patients undergoing combination therapy. However, current DDI prediction methods often overlook the interaction information between chemical substructures of drugs, focusing solely on the interaction information between drugs and failing to capture sufficient chemical substructure details. To address this limitation, we introduce a novel DDI prediction method: Multilayer Adaptive Soft Mask Graph Neural Network (MASMDDI). Specifically, we first design a multi-layer adaptive soft mask graph neural network to extract substructures from molecular graphs. Second, we employ an attention mechanism to mine substructure feature information and update latent features. In this process, to optimize the final feature representation, we decompose drug-drug interactions into pairwise interaction correlations between the core substructures of each drug. Third, we use these features to predict the interaction probabilities of DDI tuples and evaluate the model using real-world datasets. Experimental results demonstrate that the proposed model outperforms state-of-the-art methods in DDI prediction. Furthermore, MASMDDI exhibits excellent performance in predicting DDIs of unknown drugs in two tasks that are more aligned with real-world scenarios. In particular, in the transductive scenario using the DrugBank dataset, the ACC and AUROC and AUPRC scores of MASMDDI are 0.9596, 0.9903, and 0.9894, which are 2% higher than the best performing baseline. [ABSTRACT FROM AUTHOR]

Accurately predicting compound–protein interactions (CPI) is a critical task in computer-aided drug design. In recent years, the exponential growth of compound activity and biomedical data has highlighted the need for efficient and interpretable prediction approaches. In this study, we propose GraphsformerCPI, an end-to-end deep learning framework that improves prediction performance and interpretability. GraphsformerCPI treats compounds and proteins as sequences of nodes with spatial structures, and leverages novel structure-enhanced self-attention mechanisms to integrate semantic and graph structural features within molecules for deep molecule representations. To capture the vital association between compound atoms and protein residues, we devise a dual-attention mechanism to effectively extract relational features through.cross-mapping. By extending the powerful learning capabilities of Transformers to spatial structures and extensively utilizing attention mechanisms, our model offers strong interpretability, a significant advantage over most black-box deep learning methods. To evaluate GraphsformerCPI, extensive experiments were conducted on benchmark datasets including human, C. elegans, Davis and KIBA datasets. We explored the impact of model depth and dropout rate on performance and compared our model against state-of-the-art baseline models. Our results demonstrate that GraphsformerCPI outperforms baseline models in classification datasets and achieves competitive performance in regression datasets. Specifically, on the human dataset, GraphsformerCPI achieves an average improvement of 1.6% in AUC, 0.5% in precision, and 5.3% in recall. On the KIBA dataset, the average improvement in Concordance index (CI) and mean squared error (MSE) is 3.3% and 7.2%, respectively. Molecular docking shows that our model provides novel insights into the intrinsic interactions and binding mechanisms. Our research holds practical significance in effectively predicting CPIs and binding affinities, identifying key atoms and residues, enhancing model interpretability. [ABSTRACT FROM AUTHOR]

Molecular property prediction faces the challenge of limited labeled data as it necessitates a series of specialized experiments to annotate target molecules. Data augmentation techniques can effectively address the issue of data scarcity. In recent years, Mixup has achieved significant success in traditional domains such as image processing. However, its application in molecular property prediction is relatively limited due to the irregular, non-Euclidean nature of graphs and the fact that minor variations in molecular structures can lead to alterations in their properties. To address these challenges, we propose a novel data augmentation method called Mix-Key tailored for molecular property prediction. Mix-Key aims to capture crucial features of molecular graphs, focusing separately on the molecular scaffolds and functional groups. By generating isomers that are relatively invariant to the scaffolds or functional groups, we effectively preserve the core information of molecules. Additionally, to capture interactive information between the scaffolds and functional groups while ensuring correlation between the original and augmented graphs, we introduce molecular fingerprint similarity and node similarity. Through these steps, Mix-Key determines the mixup ratio between the original graph and two isomers, thus generating more informative augmented molecular graphs. We extensively validate our approach on molecular datasets of different scales with several Graph Neural Network architectures. The results demonstrate that Mix-Key consistently outperforms other data augmentation methods in enhancing molecular property prediction on several datasets. [ABSTRACT FROM AUTHOR]

Cheminformatics combines chemistry, computing, and mathematics to research and improve cancer drugs. Cheminformatics deals with graph theory and its tools. A graph invariant is a number that can only be computed via a graph. Atoms are the vertices and bonds are the edges in chemical graph theory's representation of compounds as graphs. Many topological indices have been devised to identify the physical characteristics of chemical substances. In this study, we calculated the melting point, boiling point, stable properties, surface tension, and cohesion of chemical structures of newly prepared anticancer drugs to topological invariants, K-Banhatti Sombor (KBSO) invariants, Dharwad invariants, and second-order anti-harmonic invariants (QCI). The discovery of the complex physical and chemical behavior of these chemical compounds in the human body is supported by computational studies, which are highly valued. In addition, it aids students in comprehending how these chemical structures are put together and enhanced through enhanced chemical and physical capabilities. The results of these derivations are used to model chemical structures and other network structures. [ABSTRACT FROM AUTHOR]

Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability and reactivity of compounds. In this paper, we introduce a class of molecular models, namely, the Vicsek polygon graphs, which extend the traditional Vicsek networks. We compute the Zagreb indices and the Zagreb eccentricity indices of Vicsek polygon graphs by self-similarity and the recurrence relation based on the construction of graphs. [ABSTRACT FROM AUTHOR]

In this article, we introduce a novel concept called Generalized Transmission Neighbor Indices, building upon established transmission indices. The primary focus is on two variants of these indices, denoted as T N (a , b) 1 (G) and T N (a , b) 2 (G) , which offer distinct insights into graph connectivity. The first index, T N (a , b) 1 (G) , quantifies the sum of powered vertex neighbor transmissions for connected vertices, while the second, T N (a , b) 2 (G) , calculates the product of powered vertex neighbor transmissions among connected vertices. Our investigation delves into the diverse values of parameters a and b, shedding light on the relationships between these indices and established transmission neighbor-based metrics. Bounds have been computed, and we have also explored the chemical relevance (Quantitative Structure–Property Relationship) in the context of linear monocarboxylic acids. [ABSTRACT FROM AUTHOR]

The Y-index and coindex are degree based molecular structure descriptors that have been shown to give a high degree of predictability compare to Zagreb indices and F-index and their coindices for some physicochemical properties of octane isomers. In this paper, we studied the Y -- index and Y -- coindex for certain important chemical structures like line graphs of the VC5C7[p,q] and HC5C7[p,q] nanotubes and their molecular complement graph. Moreover, we defined Y -- polynomial of graph G and applied it on the line graphs of the VC5C7[p,q] and HC5C7[p,q] nanotubes. These explicit formulae can correlate the chemical structure of molecular graph of nanotube to information about their physical structure. [ABSTRACT FROM AUTHOR]

A carbon-based material with a broad scope of favourable developments is called graphene. Recently, a graphene nanoribbon with cove-edged was integrated by utilizing a bottom-up liquid-phase procedure, and it can be geometrically viewed as a hybrid of the armchair and the zigzag edges. It is indeed a type of nanoribbon containing asymmetric edges made up of sequential hexagons with impressive mechanical and electrical characteristics. Topological indices are numerical values associated with the structure of a chemical graph and are used to predict various physical, chemical, and biological properties of molecules. They are derived from the graph representation of molecules, where atoms are represented as vertices and bonds as edges. In this article, we derived the exact topological expressions of cove-edged graphene nanoribbons based on the graph-theoretical structural measures that help reduce the number of repetitive laboratory tasks necessary for studying the physicochemical characteristics of graphene nanoribbons with curved edges.

Abstract Background Drug–drug interactions (DDI) are prevalent in combination therapy, necessitating the importance of identifying and predicting potential DDI. While various artificial intelligence methods can predict and identify potential DDI, they often overlook the sequence information of drug molecules and fail to comprehensively consider the contribution of molecular substructures to DDI. Results In this paper, we proposed a novel model for DDI prediction based on sequence and substructure features (SSF-DDI) to address these issues. Our model integrates drug sequence features and structural features from the drug molecule graph, providing enhanced information for DDI prediction and enabling a more comprehensive and accurate representation of drug molecules. Conclusion The results of experiments and case studies have demonstrated that SSF-DDI significantly outperforms state-of-the-art DDI prediction models across multiple real datasets and settings. SSF-DDI performs better in predicting DDI involving unknown drugs, resulting in a 5.67% improvement in accuracy compared to state-of-the-art methods.

Accurate predictions of molecular properties are crucial for advancements in drug discovery and materials science. However, this task is complex and requires effective representations of molecular structures. Recently, Graph Neural Networks (GNNs) have emerged as powerful tools for this purpose, demonstrating significant potential in modeling molecular data. Despite advancements in GNN predictive performance, existing methods lack clarity on how architectural choices, particularly activation functions, affect training dynamics and inference stages in interpreting the predicted results. To address this gap, this paper introduces a novel activation function called the Sine Linear Unit (SLU), aimed at enhancing the predictive capabilities of GNNs in the context of molecular property prediction. To demonstrate the effectiveness of SLU within GNN architecture, we conduct experiments on diverse molecular datasets encompassing various regression and classification tasks. Our findings indicate that SLU consistently outperforms traditional activation functions on hydration free energy (FreeSolv), inhibitory binding of human β secretase (BACE), and blood brain barrier penetration (BBBP), achieving the superior performance in each task, with one exception on the GCN model using the QM9 data set. These results underscore SLU’s potential to significantly improve prediction accuracy, making it a valuable addition to the field of molecular modeling.

Chemical graph theory is an extension of mathematical chemistry that explores chemical phenomena and entities using the conceptual frameworks of graph theory. In particular, chemical graphs are used to represent molecular structures in chemical graph theory. Edges and vertices in this chemical graph substitute for bonds and atoms, respectively. The primary data types used throughout cheminformatics to depict chemical structures are chemical graphs. The basis for (quantitative) structure-property and structure-activity predictions, a central area of cheminformatics, is laid by the computable properties of graphs. The physical characteristics of molecules are thus reflected in these graphs, which can subsequently be reduced to graph-theoretical indices or descriptors. The resolving set Z , which distinguish every pair of distinct vertices in a connected simple graph, is one of the most well-studied distance-based graph descriptors. In this manuscript, we consider the most significant variation of a metric dimension known as partition dimension and determine it for the molecular complex graph of one-pentagonal carbon nanocone (PCN). We demonstrate that all of the vertices and edges in PCN can be uniquely identified only by considering three distinct non-neighboring partition sets (minimal requirement) from PCN. [ABSTRACT FROM AUTHOR]

Reverse degree-based topological indices (RDTIs) are applied to analyze the structural properties of molecules such as gamma graphyne and armchair graphyne nanoribbons. RDTIs provide valuable information about the connectivity patterns of atoms within a molecule, aiding in understanding its chemical and physical properties. For gamma graphyne and armchair graphyne nanoribbons, RDTIs would involve calculating the contributions from various atom pairs based on the degree differences between them. These indices consider the reverse order in which degrees are subtracted. RDTIs capture important aspects of molecular structure, including branching, degree distribution, and connectivity. Using RDTIs, one can assess the complexity, stability, and other characteristics of gamma graphyne and armchair graphyne nanoribbons. This paper focus on two structures made from hexagonal honeycomb graphite lattices, like gamma graphyne, and armchair graphyne nanoribbons. The methodology used in this study is First and second reverse Gourava indices, hyper first and second reverse Gourava indices, reverse multiplicative sum connectivity Gourava index, and reverse multiplicative product connectivity Gourava. Furthermore, these indices play a vital role in quantitative structure–property relationships and offer insights into the behaviour and reactivity of these unique molecular structures. Further research and computational analysis of RDTIs will deepen our understanding of these fascinating carbon-based materials. [ABSTRACT FROM AUTHOR]

Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this article, we introduce new distance-based topological indices calculated with the $ CoM $ C o M -polynomial approach. We present an application about the compatibility of these indices with some drugs that are candidates for use in the treatment of COVID-19 with QSPR analysis. [ABSTRACT FROM AUTHOR]

Molecular descriptors are mathematical representations of molecular properties, generated through numerous algorithms. These numerical values are used to quantitatively represent the physical and chemical attributes of molecules. In the field of chemical graph theory, two indices, namely the revised Szeged index and the revised edge-Szeged index, were introduced to characterize molecular properties. The Szeged index Sz(Γ) of a simple connected graph Γ is computed by summing the products of nu(e) and nv (e) for all edges e = uv in Γ, where nu(e) denotes the number of vertices in Γ that are closer to vertex u than to vertex v, and nv (e) is defined similarly. In this paper, the role of different variants of Szeged indices in modeling different physical properties of alkanes and benzenoid hydrocarbon is investigated. Their isomer discrimination ability is also examined. In addition, we obtain lower and upper bounds on revised Szeged index, revised edge-Szeged index and the difference between vertex-edge Szeged index and edge-vertex Szeged index of bicyclic graphs. [ABSTRACT FROM AUTHOR]

Topological indices are numerical values related to a chemical structure that describes the correlation of chemical structure with different physical properties and chemical reactions. Glass has wide applications in architecture, tableware, optics, and optoelectronics. In this article, first, the mathematical relationship between M-polynomial and Banhatti indices such as K-Banhatti, δ-Banhatti, and hyper δ- Banhatti indices are obtained. Then using M-polynomial, Banhatti indices are obtained. [ABSTRACT FROM AUTHOR]

The COVID-19 outbreak has appeared as a matchless global threat against all humanity. Even the most developed countries have been shocked by the adversities of the COVID-19 pandemic affecting social life, especially human health. All over the world, researchers still have been studying to develop new medicines the combat outbreak. A topological index can be thought of as the conversion of a chemical structure to a real number. Topological indices are often used to provide information about the physicochemical properties and biological properties of molecules. Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this study, we construct some new topological coindices and define the concept of CoNM -polynomial. Owing to these polynomials we pass the difficulty of calculating the topological coindices. The computing process is done for the molecular graph structure of fixed analogs of Lopinavir, Favipiravir and Ritonavir. Afterward, obtained values are evaluated in QSPR modeling via linear and quadratic regression analysis to examine some physicochemical properties of the analog medicines such as enthalpy of vaporization (E), flash point (FP), molar refractivity (MR), polarizability (P), surface tension (T), molar volume (MV). [ABSTRACT FROM AUTHOR]

Degree-based topological descriptors of chemical structures may help to measure the physico-chemical and nano-properties, which are necessary for the growing industry. Hexaphenylbenzene is a chemical structure that plays a significant role in a wide variety of applications in organic electronic materials and liquid crystals, crystal engineering, and other polymeric materials, which are among the most active research areas of investigation in chemistry, biology, and drugs. In this study, in view of the mathematical formulation and analysis of structures, some topological descriptors of the chain molecular graph of hexaphenylbenzene Ln are studied. Moreover, using MATLAB the results are analyzed and the relationship between topological indices and polynomials in the chain of hexaphenylbenzene Ln, which portrays the physio-substance properties has been deduced. These numerical values correlate structural facts, chemical and biological activities, and physical characteristics. The results obtained could help us learn more about the properties of the chain of hexaphenylbenzene. [ABSTRACT FROM AUTHOR]

The primary area of research in all branches of science and engineering is the production of low-cost goods considering the recent global economic crisis. Making small-scale, inexpensive, light-weight and high-quality items is essential for today's and tomorrow's world. Nanotechnology is more than enough of a contributor to this whole situation. Emerging nanomaterials like Lead Sulphide (PbS) have characteristics that set them apart from traditional materials. Topological indices (TIs) are numerical values associated with chemical compounds and are widely used in quantitative structure-property/activity relationship (QSPR/QSAR) studies. These indices are very useful for the prediction of certain physio-chemical properties of chemical compounds such as boiling point, stability, strain energy, entropy, etc. The M-polynomial and NM-polynomial techniques lead us to TIs for a molecular graph in less time compared to the usual computation from their definitions. Therefore, in this study, we utilise the M-polynomial and NM-polynomial techniques to compute various degree-based and neighbourhood degree sum-based TIs of complex crystal structures of PbS. [ABSTRACT FROM AUTHOR]

Existing formats based on the simplified molecular input line entry system (SMILES) encoding and molecular graph structure are designed to encode the complete semantic and structural information of molecules. However, the physicochemical properties of molecules are complex, and a single encoding of molecular features from SMILES sequences or molecular graph structures cannot adequately represent molecular information. Aiming to address this problem, this study proposes a sequence graph cross-attention (SG-ATT) representation architecture for a molecular property prediction model to efficiently use domain knowledge to enhance molecular graph feature encoding and combine the features of molecular SMILES sequences. The SG-ATT fuses the two-dimensional molecular features so that the current model input molecular information contains molecular structure information and semantic information. The SG-ATT was tested on nine molecular property prediction tasks. Among them, the biggest SG-ATT model performance improvement was 4.5% on the BACE dataset, and the average model performance improvement was 1.83% on the full dataset. Additionally, specific model interpretability studies were conducted to showcase the performance of the SG-ATT model on different datasets. In-depth analysis was provided through case studies of in vitro validation. Finally, network tools for molecular property prediction were developed for the use of researchers. [ABSTRACT FROM AUTHOR]

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The user's interface «Nomenclature Generator» for extraction of the chemical structure information from the systematic name of organic compound represented according to IUPAC nomenclature is developed at the All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences.

Abstract Graph neural networks have recently become a standard method for analyzing chemical compounds. In the field of molecular property prediction, the emphasis is now on designing new model architectures, and the importance of atom featurization is oftentimes belittled. When contrasting two graph neural networks, the use of different representations possibly leads to incorrect attribution of the results solely to the network architecture. To better understand this issue, we compare multiple atom representations by evaluating them on the prediction of free energy, solubility, and metabolic stability using graph convolutional networks. We discover that the choice of atom representation has a significant impact on model performance and that the optimal subset of features is task-specific. Additional experiments involving more sophisticated architectures, including graph transformers, support these findings. Moreover, we demonstrate that some commonly used atom features, such as the number of neighbors or the number of hydrogens, can be easily predicted using only information about bonds and atom type, yet their explicit inclusion in the representation has a positive impact on model performance. Finally, we explain the predictions of the best-performing models to better understand how they utilize the available atomic features.

Abstract Graph theory plays an important role in modeling, designing, and analyzing the structural characteristics of any molecular structure or complex network. The numerical quantities associated with a molecular structure are called topological descriptors. These descriptors are essential for understanding the topology of molecular structures and their physicochemical properties. In this paper, we study the molecular structure of crystal carbon graphite for r-level, which is one of the most well-known allotropes of carbon. Furthermore, some topological descriptors for the molecular structure of crystal carbon graphite have been computed using degree and neighborhood degree sum-based techniques. The obtained results may be used in understanding the structural characteristics and making predictions about certain physiochemical properties of crystal carbon graphite. [ABSTRACT FROM AUTHOR]

Graph neural networks have recently become a standard method for analyzing chemical compounds. In the field of molecular property prediction, the emphasis is now on designing new model architectures, and the importance of atom featurization is oftentimes belittled. When contrasting two graph neural networks, the use of different representations possibly leads to incorrect attribution of the results solely to the network architecture. To better understand this issue, we compare multiple atom representations by evaluating them on the prediction of free energy, solubility, and metabolic stability using graph convolutional networks. We discover that the choice of atom representation has a significant impact on model performance and that the optimal subset of features is task-specific. Additional experiments involving more sophisticated architectures, including graph transformers, support these findings. Moreover, we demonstrate that some commonly used atom features, such as the number of neighbors or the number of hydrogens, can be easily predicted using only information about bonds and atom type, yet their explicit inclusion in the representation has a positive impact on model performance. Finally, we explain the predictions of the best-performing models to better understand how they utilize the available atomic features. [ABSTRACT FROM AUTHOR]

Topological indices are numerical molecular descriptors that reveals structure-property relationship of chemical structures without employing any wet lab. Among numerous kind of indices, neighborhood degree sum (NDS) based indices are recently found to be significant in explaining physico-chemical properties of molecules. The present work focuses on determining optimum values of NDS-indices for the class of silicate and oxide networks. Some general formulations of the indices are obtained first for dominating, regular triangulene, and rhombus type silicate and oxide networks, and Copper oxide network. Explicit expressions of some NDS-indices are then generated. Finally, extremal conditions for the indices are established in terms of different network parameters. A graphical comparison of the outcomes is also reported. [ABSTRACT FROM AUTHOR]

Let G be a connected graph, the sum geometric - arithmetic means index of G is defined as SGAM (G) = ∑uv ∈E(G) (√(d(u)d(v) )+ (d(v)+d(v))/ 2 ) . In this paper, the concept of sum geometric harmonic means index of a graph G, denoted by SG hm (G) is introduced and SGhm (G) of few families of graphs is computed. Further, we establish the bounds for sum geometric harmonic means index. General Terms: AMS, subject Classification 05C07; 92E10. [ABSTRACT FROM AUTHOR]

Chemical graph theory is a branch of mathematical chemistry which applies classic graph theory to chemical phenomena and entities. Graphs are extensively used in chemistry to recognise the structures of chemical compounds, with the vertices and edges denoting atoms and bonds respectively. Let Γ = (V , E) be a nth order connected graph. If the distance vectors to the vertices in an ordered subset H r of vertices can uniquely identify each vertex of the graph Γ , then the set H r is known as resolving set for the graph Γ . The resolving set H r with smallest cardinality serves as the metric basis for Γ and this cardinality of the metric basis set is termed as the metric dimension of Γ . A unique representation of chemical structures can be obtained using a resolving set. In this manuscript, the most important variant of metric dimension known as mixed metric dimension is taken into consideration and computed it for most important allotrope of carbon commonly known as crystal cubic carbon. Mixed metric dimension of Crystal Cubic Carbon structure has been computed and a comparison among metric dimension, edge metric dimension and mixed metric dimension has been done, from which we find that these three dimensions are equal. [ABSTRACT FROM AUTHOR]

Molecular descriptors are mathematical representations of molecular properties, generated through numerous algorithms. These numerical values are used to quantitatively represent the physical and chemical attributes of molecules. In the field of chemical graph theory, two indices, namely the revised Szeged index and the revised edge-Szeged index, were introduced to characterize molecular properties. The Szeged index (Γ) Sz of a simple connected graph Γ is computed by summing the products of ( ) u n e and ( ) v n e for all edges = e uv in Γ, where ( ) u n e denotes the number of vertices in Γ that are closer to vertex u than to vertex v, and ( ) v n e is defined similarly. In this paper, the role of different variants of Szeged indices in modeling different physical properties of alkanes and benzenoid hydrocarbon is investigated. Their isomer discrimination ability is also examined. In addition, we obtain lower and upper bounds on revised Szeged index, revised edge-Szeged index and the difference between vertex-edge Szeged index and edge-vertex Szeged index of bicyclic graphs. [ABSTRACT FROM AUTHOR]

The atom-bond sum-connectivity index of a graph G is defined as A B S (G) = ∑ x y ∈ E (G) d x + d y - 2 d x + d y , where d x is the degree of the vertex x in G. In this paper, we study the ABS index of unicyclic graphs with a specified girth and determine the smallest, second smallest, third smallest, and fourth smallest ABS index. We also identify the graphs that achieve these extremal values. In addition, the ABS index is found to have significant potential in structure–property modelling for some compounds containing cyclic substructures. [ABSTRACT FROM AUTHOR]

The most important application of anticancer drugs in various forms (alkylating agents, hormones agents, and antimetabolites) is the treatment of malignant diseases. Topological indices are widely used in the field of chemical and medical sciences, especially in studying the chemical, biological, clinical, and therapeutic aspects of drugs. In this article, the temperature indices in anticancer drugs molecular graphs such as Carmustine, Convolutamine F, Raloxifene, Tambjamine K, and Pterocellin B were calculated and then analyzed based on physical and chemical properties. The analysis was performed by identifying the best regression models based on temperature indices for six physical and chemical features of anticancer drugs. The results indicated that temperature indices were essential topological indices that predict the properties of anticancer drugs, such as boiling point, flash point, enthalpy, molar refractivity, molar volume, and polarizability. It was also observed that the r value of the regression model was more than 0.6, and the p value was less than 0.05.

Drug–drug interaction (DDI) identification is essential to clinical medicine and drug discovery. The two categories of drugs (i.e. chemical drugs and biotech drugs) differ remarkably in molecular properties, action mechanisms, etc. Biotech drugs are up-to-comers but highly promising in modern medicine due to higher specificity and fewer side effects. However, existing DDI prediction methods only consider chemical drugs of small molecules, not biotech drugs of large molecules. Here, we build a large-scale dual-modal graph database named CB-DB and customize a graph-based framework named CB-TIP to reason event-aware DDIs for both chemical and biotech drugs. CB-DB comprehensively integrates various interaction events and two heterogeneous kinds of molecular structures. It imports endogenous proteins founded on the fact that most drugs take effects by interacting with endogenous proteins. In the modality of molecular structure, drugs and endogenous proteins are two heterogeneous kinds of graphs, while in the modality of interaction, they are nodes connected by events (i.e. edges of different relationships). CB-TIP employs graph representation learning methods to generate drug representations from either modality and then contrastively mixes them to predict how likely an event occurs when a drug meets another in an end-to-end manner. Experiments demonstrate CB-TIP 's great superiority in DDI prediction and the promising potential of uncovering novel DDIs. [ABSTRACT FROM AUTHOR]

One of the major branches of mathematical chemistry is the chemical graph theory that employs graph invariants to demonstrate chemical phenomena mathematically. Topological indices are numerical graph invariants derived from molecular graph representations of chemical compounds that are used in structure–property modelling. In a brief span of time, the Zagreb connection indices have garnered a lot of attention. The ultimate goal of the present report is to reveal the chemical significance of this variants of Zagreb index and to demonstrate their fascinating mathematical attributes. The chemical connection of the indices is examined by investigating their potential in structure–property modelling. To illustrate mathematical features, some crucial upper bounds for connection indices are computed with characterizing maximal structures. The maximal graphs for the class of connected, tree, bipartite and chain graphs are identified by means of connection indices in terms of graph order. Such characterization is quite useful in regulating molecular properties that the connection indices can predict. [ABSTRACT FROM AUTHOR]

Topological indices serve as mathematical tools for characterising the molecular structure of a compound, and are useful to anticipate its properties. Actually, these are quantitative measures that can provide valuable information regarding the structure of a molecule, such as its connectivity and symmetry. By analysing these indices, researchers can make predictions about the behaviour of the molecule, such as its reactivity, solubility, and toxicity, among others. The γ-Graphyne is a fascinating carbon allotrope that has recently gained significant attention due to its unique electronic, optical, and mechanical properties. As a result, there has been increasing interest in exploring its potential applications in various fields of science and technology. The molecular descriptors for the characterisation of γ-Graphyne have not yet been investigated. Therefore, it is of much importance to predict its molecular topology to well understand the physicochemical properties. In this work, a graph theory-based edge partitioning technique is used to model the molecular topology of γ-Graphyne and Zigzag graphyne nanoribbon, and mathematical closed-form expressions for some of its essential degree-based molecular descriptors are derived. These computed indices have been illustrated with the help of graphical representations and numerical tables. [ABSTRACT FROM AUTHOR]

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose d G (v i) is degree of the vertex v i for each i = 1 , 2 , ... , n . Now, the k-th degree-based graph entropy for G is defined as I d , k (G) = − ∑ i = 1 n d G (v i) k ∑ j = 1 n d G (v j) k l o g d G (v i) k ∑ j = 1 n d G (v j) k , where k is real number. The first-degree-based entropy is generated for k = 1 , which has been well nurtured in last few years. As ∑ j = 1 n d G (v j) k yields the well-known graph invariant first Zagreb index, the I d , k for k = 2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of I d , 2 in structure property modeling of molecules. [ABSTRACT FROM AUTHOR]