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A distance-related spectral descriptor is a graphical index with defining structure built on eigenvalues of chemical matrices relying on distances in graphs. This paper explores the predictive ability of both existing and new distance-related spectral descriptors for estimating thermodynamic characteristics of polycyclic hydrocarbons (PHs). As a standard choice, the entropy and heat capacity are selected to represent thermodynamic properties. Furthermore, 30 initial members of PHs are considered as test molecules for this study. Three new molecular matrices have been proposed and our research demonstrates that distance-spectral graphical indices built by these novel matrices surpass in efficiency relative to famous distance-spectral indices. First, a novel computational method is put forwarded to evaluate distance-spectral indices of molecular graphs. The proposed methodology is utilized to compute both pre-existing and novel distance-related spectral descriptors, with an aim to assess their predictive efficacy using experimental data pertaining to two selected thermodynamic properties. Subsequently, we identify the five most promising distance-related spectral descriptors, comprising the degree-distance and Harary energies, the recently introduced second geometric-arithmetic energy along with its associated Estrada invariant, and 2 atom-bond connectivity (ABC) Estrada index. Notably, the 2 ABC Estrada index and Harary energy demonstrate correlation coefficients exceeding 0.95, while certain conventional spectral indices including the distance energy as well as its associated Estrada index, display comparatively lower performance levels. Moreover, we illustrate the practical implications of our findings on specific classes of one-hexagonal nanocones and carbon polyhex nanotubes. These outcomes hold potential for enhancing the theoretical determination of certain thermodynamic attributes of these nanostructures, offering improved accuracy and minimal margin of error. [ABSTRACT FROM AUTHOR]

Abstract In the fields of mathematics, chemistry, and the physical sciences, graph theory plays a substantial role. Using modern mathematical techniques, quantitative structure-property relationship (QSPR) modeling predicts the physical, synthetic, and natural properties of substances based only on their chemical composition. For a chemical graph, the temperature of a vertex is a local property introduced by Fajtlowicz (1988). A temperature-based graphical descriptor is structured based on temperatures of vertices. Involving a non-zero real parameter $$\beta$$ β , the general F-temperature index $$T_{\beta }$$ T β is a temperature index having strong efficacy. In this paper, we employ discrete optimization and regression analysis to find optimal value(s) of $$\beta$$ β for which the prediction potential of $$T_{\beta }$$ T β and the total $$\pi$$ π -electron energy $$E_{\pi }$$ E π of polycyclic hydrocarbons is the strongest. This, in turn, answers an open problem proposed by Hayat & Liu (2024). Applications of the optimal values for $$T_{\beta }$$ T β are presented a two-parametric family of carbon nanocones in predicting their $$E_{\pi }$$ E π with significantly higher accuracy.

Abstract A distance-related spectral descriptor is a graphical index with defining structure built on eigenvalues of chemical matrices relying on distances in graphs. This paper explores the predictive ability of both existing and new distance-related spectral descriptors for estimating thermodynamic characteristics of polycyclic hydrocarbons (PHs). As a standard choice, the entropy and heat capacity are selected to represent thermodynamic properties. Furthermore, 30 initial members of PHs are considered as test molecules for this study. Three new molecular matrices have been proposed and our research demonstrates that distance-spectral graphical indices built by these novel matrices surpass in efficiency relative to famous distance-spectral indices. First, a novel computational method is put forwarded to evaluate distance-spectral indices of molecular graphs. The proposed methodology is utilized to compute both pre-existing and novel distance-related spectral descriptors, with an aim to assess their predictive efficacy using experimental data pertaining to two selected thermodynamic properties. Subsequently, we identify the five most promising distance-related spectral descriptors, comprising the degree-distance and Harary energies, the recently introduced second geometric-arithmetic energy along with its associated Estrada invariant, and 2 $$\text {nd}$$ atom-bond connectivity (ABC) Estrada index. Notably, the 2 $$\text {nd}$$ ABC Estrada index and Harary energy demonstrate correlation coefficients exceeding 0.95, while certain conventional spectral indices including the distance energy as well as its associated Estrada index, display comparatively lower performance levels. Moreover, we illustrate the practical implications of our findings on specific classes of one-hexagonal nanocones and carbon polyhex nanotubes. These outcomes hold potential for enhancing the theoretical determination of certain thermodynamic attributes of these nanostructures, offering improved accuracy and minimal margin of error.

In this manuscript, we delve into the exploration of the first and second Zagreb connection indices of both polyomino chains and random polyomino chains. Our methodology relies on the utilization of Markov chain theory. Within this framework, the article thoroughly examines precise formulas and investigates extreme values. Leveraging the derived formulas, we further explore and elucidate the long-term behavior exhibited by random polyomino chains.

Abstract Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide $$({\text{InP}})$$ ( InP ) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide $$({\text{InP}})$$ ( InP ) .

Indium phosphide (InP) is a binary semiconductor composed of indium and phosphorus. It has a zinc blende crystal structure, which is a type of cubic lattice structure. This lattice is composed of indium and phosphorus atoms arranged in a lattice of cube-shaped cells, with each cell containing four indium atoms and four phosphorus atoms. This lattice structure is the same for all materials with a zinc blende crystal structure and is the most common type of lattice structure in semiconductors. Indium phosphide (InP) has several chemical applications. It is commonly used as a dopant in the production of semiconductors, where it helps control the electrical properties of the material. InP is also utilized in the synthesis various indium-containing compounds, which can have applications in catalysts and chemical reactions. Additionally, InP nanoparticles have been investigated for their potential use in biomedical imaging and drug delivery systems. The topological characterization of 3D molecular structures can be performed via graph theory. In graph theory, the connections between atoms are represented as edges and the atoms themselves are represented as nodes. Furthermore, graph theory can be used to calculate the topological descriptors of the molecule such as the degree-based and reverse degree-based irregularity toplogical indices. These descriptors can be used to compare the topology of different molecules. This paper deals with the modeling and topological characterization of indium phosphide (InP) via degree-based and reverse irregularity indices. The 3D crystal structure of the InP is topologically modeled via partition of the edges, and derived closed form expressions for its irregularity indices. Our obtained results will be surely be helpful in investigating the QSPR/QSAR analysis as well as understanding the deep irregular behavior of the indium phosphide (InP) . [ABSTRACT FROM AUTHOR]

In a graph G=(V,E), the temperature Tx of a vertex x∈V is defined as Tx=dx/n−dx, where n is the order of G and dx is the valency/degree of x. A topological/graphical index GI is a map GI:∑→ℝ, where ∑ (respectively, ℝ) is the set of simple connected graphs (respectively, real numbers). Graphical indices are employed in quantitative structure-property relationship (QSPR) modeling to predict physicochemical/thermodynamic/biological characteristics of a compound. A temperature-based graphical index of a chemical graph G is defined as GIT:=∑edgesf(Tx,Ty), where f(Tx,Ty) is a symmetric 2-variable map. In this paper, we introduce two new novel temperature-based indices named as the reduced reciprocal product-connectivity temperature (RRPT) index and the geometric-arithmetic temperature (GAT) index. The predictive potential of these indices has been investigated by employing them in structure-property modeling of the total π-electronic energy Eπ(β) of benzenoid hydrocarbons. In order to validate the statistical inference, the lower 30 BHs have been opted as test molecules as their experimental data for Eπ(β) is also publicly available. First, we employ a computer-based computational method to compute temperature indices of 30 lower BHs. Certain QPSR models are proposed by utilizing the experimental data of Eπ for the BHs. Our statistical analysis suggests that the most efficient regression models are, in fact, linear. Our statistical analysis asserts that both RRPT and GAT outperformed all the existing temperature indices for correlating Eπ for the BHs. The results suggest their further employability in QSPR modeling. Importantly, our research contributes toward countering proliferation of graphical indices. [ABSTRACT FROM AUTHOR]

Carbon nanowires based on various structures have various applications. In this article, our focus is on diamond nano‐wires, based on the structure of the diamond. Our goal is to characterize these nanowires by providing their hyper‐Wiener index, one of the basic topological graph indices. The diamond is formed by carbon atoms in a compact structure: every atom has exactly four neighbors connected by covalent bonds according to the simplest three‐dimensional polyhedron. Considering an atom in the center of a tetrahedron, its neighbors, the atoms connected to it by bonds, are located in the corners of the tetrahedron. In this article, this "diamond‐grid" structure is analysed in the case that the graphs correspond to connected parts of sequences of unit cells, in this way forming nanowires of various lengths. By a combinatorial approach, a closed formula is proven for the hyper‐Wiener index based on the graph‐distances of every pair of carbon atoms (i.e., the minimal number of edges connecting the atoms), and this formula depends only on the size of the graph in terms of the number of unit cells included. [ABSTRACT FROM AUTHOR]

A topological index is a number that is connected to a chemical composition in order to correlate a substance's chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay's originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs. [ABSTRACT FROM AUTHOR]

The reactions of N-p-carboxyphenyl-β-D-glucopyranosylamine and N-p-carboxyphenyl-β-D-galactopyranosylamine with dicyclohexylcarbodiimide in the presence of tetrahydrofuran and triethylamine were studied for the first time. Interaction of the synthesised acylureas with sodium nitrite was used to obtain glycosylamines containing a nitroso (N=O) group. The synthesised compounds were studied within the framework of mathematical chemistry, using the method of quasi-PNS-matrices (PNS-). The influence of compounds: b-N-(p-carboxyphenylgalactopyranosyl)- acylurea and b-N-(p-carboxyphenylgalactopyranosyl)-nitrosourea on the growth and development of microorganism has been investigated. The antimicrobial properties of the synthesised compounds were studied on various microorganisms. [ABSTRACT FROM AUTHOR]

Several chemical and medical experimentation reveals a dependence of physicochemical and biological properties of a compound on its molecular structure. Molecular/topological descriptors/indices retrieve this dependence by employing mathematical/statistical tools to generate quantitative structure property/activity relationship (QSAR/QSPR) models. QSAR/QSPR models are regression models which theoretically relate a physicochemical/biological property to a molecular descriptor. By converting a compound to a chemical graph, graph-theoretic topological indices use algorithmic graph theory to generate QSAR/QSPR models. Degree-related molecular indices have been well-known for correlating better with certain physicochemical characteristics of compounds. In this paper, we conduct a comparative analysis to put forward the best degree-based index for correlating with physicochemical characteristics of polycyclic aromatic hydrocarbons. Two different computational techniques have been put forward and then used to conduct our comparative analysis. Our comparative testing generates several favorable and unexpected conclusions as the well-known indices such as the augmented Zagreb index, the atom-bond connectivity index, the geometric arithmetic index deliver relatively poor performance. Moreover, exceptional performance of the generalized variants of Randić and sum-connectivity indices is somehow unexpected as they significantly outperform the well-studied and well-researched degree-based indices. This warrants to study further the general Randić and sum-connectivity indices for QSAR/QSPR models. Applications to certain families of carbon polyhex aromatic nanotubes are reported. [ABSTRACT FROM AUTHOR]

In the past few years, two-dimensional (2D) layered nanomaterials have greatly attracted the scientific community. Among 2D nanomaterials, the porphyrin-based Naphtalenic nanosheets have been the subject of intense research due to their utilization in photo-dynamic therapy and nanodevices. New technologies based on nanomaterials or Naphtalenic nanosheet are advantageous in overcoming the problems in conventional drug delivery like poor solubility, toxicity and poor release pattern of drugs. In chemical network theory, various molecular descriptors are used to predict the chemical properties of molecules; these molecular descriptors are found to be very useful for Quantitative Structure–Activity/ Quantitative Structure–Property (QSAR/QSPR) relationship analysis in materials engineering, chemical and pharmaceutical industries. Researchers have computed the molecular descriptors for various nanostructures; however, despite intense research, the topology of nanostructures is not yet well understood. Specially, to our knowledge, the computation of topological indices for the line graph of subdivision graph of H-Naphtalenic nanosheet has not been discussed so far, which may open new perspectives for a more accurate and reliable topological characterization of this nanosheet. In this article, we employed some important degree-based topological indices to study the chemical structure of Naphtalenic nanosheet as a chemical network for QSAR/QSPR analysis. We have computed these degree-based topological indices for the line graph of subdivision graph of H-Naphtalenic nanosheet and derived formulas for them. Based on the derived formulas, numerical results are obtained and the physical and chemical properties of the under study nanosheet are investigated. [ABSTRACT FROM AUTHOR]

In this article, the efficiency of all the well-known valency-based molecular descriptors has been measured using certain comparative testing. Importantly, we use a computational technique for hexagonal systems to generate regression models to determine the correlation of valency-based molecular descriptors with the π-electronic energies for polycyclic aromatic hydrocarbons. The study implicates some favorable outcomes as the sum-connectivity index and certain Randić index have correlation coefficient of 0.9999. To ensure the applicability of our proposed study, we compute analytically explicit expressions for efficient valency-based molecular descriptors for certain infinite families of carbon nanotubes and carbon nanocones. Our results assist in correlating the π-electronic energies of underlying chemical structures of these nanotubes and nanocones. [ABSTRACT FROM AUTHOR]

Objectives. This article aims to describe, elaborate, and test a general algorithmic method for constructing the structure–property models for organic compounds.Results. The construction of the models is based on the statistical analysis of some sets of chemical structures of definite classes with known property values. These models have some forms of correlation equations. For the representation of chemical structures in this method, the special weighted molecular graphs (MGs) that reflect some peculiarities of the spatial structures of the corresponding molecules are used. The proposed method is realized in two steps. First, it is assumed that the required structure–property equation has a definite form and depends on several adjusted numerical parameters and two changeable functions of one variable. In this step, from some set of functions, the pair of functions that provide the best model is selected. In the second step, the best model (from the previous step) is modified. For this purpose, the classification of the vertices of MG by the chemical symbols of the corresponding atoms and their first-order environments is fulfilled. Further, the graph edges are classified according to the classes of the vertices which they connect. Furthermore, the numerical correction terms for the initial weights of the vertices and edges are introduced, and they improve the obtained model. The final result of the model-construction process is the equation of the definite form containing concrete numerical values of its parameters. Some examples of the application of the elaborated method for constructing the structure–property models for the concrete properties and classes of compounds are presented. The following classes of organic compounds and their physicochemical properties are considered: 1) the boiling point of alcohols, 2) the water solubility of alcohols, 3) the boiling point of sulfides, and 4) the retention indices of alkylphenols. The obtained results indicate the efficiency of the proposed approach and the significance of introducing the second step to the method.Conclusions. In this work, a general algorithmic and computerized method for constructing the structure–property models of organic compounds is suggested. Examples of the application of this method demonstrated its high efficiency. The method is suitable for any class of organic compounds and properties, which are quantitatively measured. Owing to its high efficiency, the structure–property models obtained by this approach can be employed to calculate the properties of chemical compounds for which experimental data are unavailable.

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and is considered by some as one of the most intriguing open problems in mathematical chemistry. In this paper, we describe the exact structure of the extremal trees with sufficiently many vertices and we show how their structure evolves when the number of vertices grows. An interesting fact is that their radius is at most 5 and that all vertices except for one have degree at most 54. In fact, all but at most O (1) vertices have degree 1, 2, 4, or 53. Let γ n = min ⁡ { ABC (T) : T is a tree of order n }. It is shown that γ n = 1 365 1 53 (1 + 26 55 + 156 106) n + O (1) ≈ 0.67737178 n + O (1). [ABSTRACT FROM AUTHOR]

A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs and other chemical substances as different forms, trees, and graphs. Certain physico-chemical features of chemical substances correlate better with degree-based topological invariants. Predictions concerning the dynamics of the continuing pandemic may be made with the use of the graphic theoretical approaches given here. In Networks, the degree entropy of the epidemic and related trees was computed. It highlights the essay’s originality while also implying that this piece has improved upon prior literature-based realizations. In this paper, we study an important degree-based invariant known as the inverse sum indeg invariant for a variety of graphs of biological interest networks, including the corona product of some interesting classes of graphs and the pandemic tree network, curtain tree network, and Cayley tree network. We also examine the inverse sum indeg invariant features for the molecular graphs that represent the molecules in the bicyclic chemical graphs.

For the structure–property modeling of thermodynamic properties of polycyclic aromatic hydrocarbons (PAHs), this paper explores the effectiveness of a specific class of graphical indices defined based on eigenvalues, also known as valency-spectral graphical indices. The 30 lower PAHs have been selected as test molecules. The heat capacity (C p) and entropy (S o) are the standard choices for characterizing thermodynamic properties due to their close correlation with the thermodynamic properties of a similar nature. A computer-dependent method is proposed to calculate valency-spectral indices of chemical graphs, and it is employed to compute the indices for our test molecules. The statistical inferences reveal an unexpected finding for the Estrada harmonic energy, a less familiarized spectral descriptor within the research community, outperforming all the existing descriptors, followed by the positive & negative inertia indices. The Estrada harmonic energy achieved the highest mean correlation coefficient of ρ > 0. 99. On the other hand, well-studied descriptors such as Laplacian energy and adjacency energy still maintained their effectiveness in correlating the thermodynamic properties of PAHs; however, they were significantly outperformed by the Estrada harmonic energy. The three best valency-spectral indices are employed in the structure–property modeling of thermodynamic properties of linear polyacenes. [Display omitted] [ABSTRACT FROM AUTHOR]

Quantitative structure-activity and structure-property associations of natural systems require terminologies for their topological properties. Structure-based topological descriptors/indices of these systems allow these chemical possessions and the bioactivities of these compounds through reckonable structure-activity and structure-property associations' procedures. In this paper, we propose a computational technique to compute analytically exact expressions for certain degree and distance-based topological indices for general graphs. A comparative analysis is conducted with the known techniques where certain experiments are performed to show that our technique is more efficient and possesses less algorithmic and computational complexity. We apply our method to compute explicit expressions of certain degree and distance topological indices for certain infinite families of fullerenes, carbon nanotubes, and carbon nanocones. The obtained results in this paper generalize certain known results in the literature.

• New matrix functions of the adjacency matrix are proposed based on graph spectral folding. • The graph spectrum is folded at two reference eigenvalues giving them the maximal priority in the matric function. • The new matrix functions account for the significance of HOMO and LUMO in chemical reactivity. • The carcinogenicity of polycyclic aromatic compounds is very well described by the new double Gaussianized matrix function. The graph spectrum is the set of eigenvalues of a simple graph with n vertices. Here we fold this graph spectrum at a given pair of reference eigenvalues and then exponentiate the resulting folded graph spectrum. This process produces double Gaussianized functions of the graph adjacency matrix which give more importance to the reference eigenvalues than to the rest of the spectrum. Based on evidences from mathematical chemistry we focus here our attention on the reference eigenvalues ± 1. In the examples that we have examined, they enclose most of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of organic molecular graphs. We prove here several results for the trace of the double Gaussianized adjacency matrix of simple graphs–the double Gaussianized Estrada index. Finally we apply this index to the classification of polycyclic aromatic hydrocarbons (PAHs) as carcinogenic or inactive ones. We discover that local indices based on the previously developed matrix function allow to classify correctly 100% of the PAHs analyzed. Such indices reflect the electron population of the HOMO/LUMO and eigenvalues close to them, in the so-called K and L regions of PAHs. [ABSTRACT FROM AUTHOR]

New chemistry, the chemistry of the 20th century, developed through four revolutions (instrumental, theoretical, biological, and informational). This development was also evident in Croatia, especially after WWII, when many young Croatian chemists had been educated at British, American, but also Russian universities. This led to the clash of old, traditional (K. Balenović), and young, modern chemists (M. Randić, N. Trinajstić), who introduced theoretical (computational), quantum, and mathematical chemistry in Croatia. There were two aspects of the clash. The first was fundamental; traditional chemists were unable to comprehend chemical research without a chemical laboratory. The second, pragmatic aspect of the clash, materialized in scientometrics, i.e. discussions about the value of chemical research in terms of the number of published papers. Theoretical chemists, namely, published much more than their colleagues engaged in laboratory practice, mostly because of scarce resources and bad organization of scientific research in communist Yugoslavia (1945–1991). [ABSTRACT FROM AUTHOR]

This paper presents a novel and generalised mathematical formulation for mathematical and theoretical chemistry. The formulation presented employs network theoretic methods and standard Conformal Geometric Algebra (Conformal Clifford Algebra) with a unique algebraic extension that introduces special non-integer basis vectors, known as 'shades'. The methodology developed lays preliminary foundations for both generic and more specialised characterisations and modelling of chemical systems by computing a multi-vector function, termed the 'hyperfield' (an algebra-geometric characterisation of a many-agent chemical system). In this paper, the formulation has been applied to inorganic compounds, in the context of their emergent properties (such as boiling and melting points) and intra-molecular characteristics. Case studies have been presented for the calculation of melting point, boiling point, maximum solubility in water and equilibrium bond length of 21 diatomic molecules. This work finds that a network theoretic model of many-agent systems modelled in R 4 , 1 space, using an algebraic extension of non-integer basis vectors, presents a promising and unifying method for theoretical mathematical chemistry. [ABSTRACT FROM AUTHOR]

Chemical clock reactions are characterized by a relatively long induction period followed by a rapid ‘switchover’ during which the concentration of a clock chemical rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis, the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via ‘kitchen sink chemistry’ experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry.

This study is devoted to the mathematical description of a kinetic experiment under the setting of multiple solutions to the inverse problems of chemical kinetics. A new algorithm for the global search of uncertainty domains is proposed, which represents a symbiosis of the methods of global optimization with an interval evolutionary approach. Chemical reaction models built using the kinetic parameters of these areas describe experimental data within an acceptable measurement error specified by the researcher. The use of this algorithm allows a complex multidimensional domain in the global space of kinetic parameters, whereas the local solution sets describing the experimental data with near equal accuracy are searched or the one-, two-, or three-dimensional projections of uncertainty domains are separately built in many other studies. The proposed algorithm has been tested using a reaction simulation of n-decane inhibited oxidation. Since this structure has a formal parallelism, parallel computing techniques are applied to speed up calculations. [ABSTRACT FROM AUTHOR]

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy S o and the heat capacity C p have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both C p and S o is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity (A B C 2 ) index, the total eccentricity (ζ) index, and the eccentric-connectivity (ξ) index outperform the well-researched descriptors such as the Szeged (S z), the Wiener W , the Padmakar-Ivan (P I) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the A B C 2 index showcases the mean correlation coefficient ρ > 0. 95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy S o and the heat capacity C p of linear polyacenes. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper employs valency descriptors to investigate their predictive potential for determining thermodynamic properties of benzenoid hydrocarbons. It is customary to choose the heat capacity (C p) and the entropy (S o) to be the representatives of thermodynamic properties. First we put forward a theoretical (resp. computer-based computational) technique for hexagonal systems (resp. general chemical graphs) for computing valency descriptors. The theoretical technique is employed in the comparative testing of valency descriptors for measuring C p and S o of lower benzenoid hydrocarbons (BHs). Our statistical experiments showcase some unexpected outcomes as the best descriptors for correlating physcochemical properties perform rather poorly for the case of thermodynamic properties. Moreover, some under-researched descriptors such as the general sum-connectivity and the general Randić descriptors perform exceptionally well. The well-performing valency descriptors are computed for some families of silicon carbide nanotubes which could be utilized to correlate their thermodynamic properties. [Display omitted] • A theoretical method to calculate valency descriptors for hexagonal systems is proposed. • A computer-based computational technique is proposed for general chemical graphs. • Comparative analysis of valency descriptors for correlating thermodynamic properties of PAHs is conducted. • Generalized Randić & sum-connectivity descriptors outperform well-established ABC, GA & AZI descriptors. • Applications of well-performing descriptors are presented for families of silicon carbide nanotubes. [ABSTRACT FROM AUTHOR]

A topological descriptor/index (or molecular structure descriptor) is a numerical value associated with chemical constitution for correlation of chemical structure/network with various physical properties, chemical reactivity or biological activity. Quantitative structure–activity and structure–property relationships of chemical networks require expressions for the topological properties of these networks. Topological indices provide these expressions of topological properties. Valency-based topological descriptors are the oldest and most successful class of descriptors so far. A chemical graph/network is a representation of the structural formula of a chemical compound whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. In this paper, we study valency-based topological indices of chemical networks. By using some real world data, we performed certain comparative testings to investigate the performance of almost all well-known valency-based indices. Dependence on the molecular structure is studied for topological indices which are best in performance. We calculated explicit formulas for well-performed indices of some infinite families of carbon nanotubes, carbon nanocones and a newly proposed family of organic networks called tetrahedral diamond networks. Tetrahedral diamond networks arises by recurrently joining graphene layers in a diamond cluster. Significance and applicability of the obtained results are reported. [ABSTRACT FROM AUTHOR]