Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

Modified reverse degree descriptors for combined topological and entropy characterizations of 2D metal organic frameworks: applications in graph energy prediction

Topological descriptors are widely utilized as graph theoretical measures for evaluating the physicochemical properties of organic frameworks by examining their molecular structures. Our current research validates the usage of topological descriptors in studying frameworks such as metal-butylated hydroxytoluene, NH-substituted coronene transition metal, transition metal-phthalocyanine, and conductive metal-octa amino phthalocyanine. These metal organic frameworks are crucial in nanoscale research for their porosity, adaptability, and conductivity, making them essential for advanced materials and modern technology. In this study, we provide the topological and entropy characterizations of these frameworks by employing robust reverse degree based descriptors, which offer insightful information on structural complexities. This structural information is applied to predict the graph energy of the considered metal organic frameworks using statistical regression models.

Predicting enthalpy of formation of benzenoid hydrocarbons and ordering molecular trees using general multiplicative Zagreb indices

Many existing studies show that there exists a strong relationship between structures and characteristics of molecules. Topological indices are often used in modeling the properties of chemical compounds and biological activities in theoretical chemistry. Topological indices are numerical values associated with structures of molecules in such a way that they remain constant under graph isomorphism. Multiplicative Zagreb indices are among the famous topological indices that have been explored by numerous researchers in the last few years. The first objective of the present paper is to examine the importance of general multiplicative Zagreb indices for forecasting the enthalpy of formation of hydrocarbons using a data set of 25 benzenoid hydrocarbons. The second objective of this paper is to study molecular trees with a given order and with a given number of branching vertices or segments using general multiplicative (first and second) Zagreb indices. Sharp lower/upper bounds on these Zagreb indices for the aforementioned molecular trees are obtained and the graphs attaining these bounds are determined. Bounds on the classical multiplicative Zagreb and Narumi-Katayama indices are corollaries of the obtained results.

Analyzing the expected values of neighborhood degree-based topological indices in random cyclooctane chains

Cyclooctane is classified as a cycloalkane, characterized by the chemical formula C 8 H 16. It consists of a closed ring structure composed of eight carbon atoms and sixteen hydrogen atoms. A cyclooctane chain typically refers to a series of cyclooctane molecules linked together. Cyclooctane and its derivatives find various applications in chemistry, materials science, and industry. Topological indices are numerical values associated with the molecular graph of a chemical compound, predicting certain physical or chemical properties. In this study, we calculated the expected values of degree-based and neighborhood degree-based topological descriptors for random cyclooctane chains. A comparison of these topological indices' expected values is presented at the end.

On quantitative structure-property relationship (QSPR) analysis of physicochemical properties and anti-hepatitis prescription drugs using a linear regression model

Numerous studies demonstrate a strong intrinsic relationship between the boiling and melting temperatures, among other chemical properties, of chemical compounds and pharmaceutical and their molecular structures. Using topological indices, researchers can learn more about the physical traits, chemical stability, and bioactivities of these chemical molecular structures. Topological indices on the chemical structure of chemical materials and drugs are investigated in order to make up for the absence of chemical experiments and provide a theoretical basis for the manufacture of medications and chemical materials. According to well-known degree-based topological indices, the chemical structures of drugs used to treat hepatitis (A, B, C, D, and E) are assessed in this study. The atoms are thought of as the vertices of a graph, and the borders that separate them are thought of as the edges. Using degree-based topological indices, a quantitative structure-property relationship (QSPR) investigation was conducted to predict the physical properties of 16 hepatitis medications. These topological indices link the chemical structure to specific physical characteristics, such as the surface tension of hepatitis medication molecules and molecular weight, enthalpy, boiling point, density, vapor pressure, and logP. Using their molecular structures, the study's drugs are represented as molecular graphs, and 14 topological indices are computed.

Peak Scores Significantly Depend on the Relationships between Contextual Signals in ChIP-Seq Peaks

Chromatin immunoprecipitation followed by massively parallel DNA sequencing (ChIP-seq) is a central genome-wide method for in vivo analyses of DNA-protein interactions in various cellular conditions. Numerous studies have demonstrated the complex contextual organization of ChIP-seq peak sequences and the presence of binding sites for transcription factors in them. We assessed the dependence of the ChIP-seq peak score on the presence of different contextual signals in the peak sequences by analyzing these sequences from several ChIP-seq experiments using our fully enumerative GPU-based de novo motif discovery method, Argo_CUDA. Analysis revealed sets of significant IUPAC motifs corresponding to the binding sites of the target and partner transcription factors. For these ChIP-seq experiments, multiple regression models were constructed, demonstrating a significant dependence of the peak scores on the presence in the peak sequences of not only highly significant target motifs but also less significant motifs corresponding to the binding sites of the partner transcription factors. A significant correlation was shown between the presence of the target motifs FOXA2 and the partner motifs HNF4G, which found experimental confirmation in the scientific literature, demonstrating the important contribution of the partner transcription factors to the binding of the target transcription factor to DNA and, consequently, their important contribution to the peak score.

Connection number topological aspect for backbone DNA networks

The present study investigates the complex topological characteristics of DNA networks, with a specific emphasis on the innovative metric known as Connection Number (CN) as a key factor in determining network structure. The Connection Number, represented as CN(v) for a vertex v, measures the count of unique paths that link v to every other vertex in the network. By employing rigorous mathematical modeling and analysis techniques, we are able to reveal the profound implications of CN (complex networks) in characterizing the structural robustness and dynamics of information flow within DNA networks. The study of how the theory of graphs and chemicals interact is known as chemical graph theory. This paper, computing the hyper Zagreb connection index, augmented connection index, inverse sum connection index, harmonic connection index, symmetric division connection index, geometric arithmetic connection index, and atom bond connectivity connection index, of two significant types of backbone DNA and Barycentric subdivision of backbone DNA networks. Direct method computation is used to produce these Connection-based topological descriptors.

On reciprocal degree distance of graphs

Given a connected graph H, its reciprocal degree distance is defined asRDD(H)=∑x≠ydH(vx)+dH(vy)dH(vx,vy), where dH(vx) denotes the degree of the vertex vx in the graph H and dH(vx,vy) is the shortest distance between vx and vy in H. The goal of this paper is to establish some sufficient conditions to judge that a graph to be ħ-hamiltonian, ħ-path-coverable or ħ-edge-hamiltonian by employing the reciprocal degree distance.

Comparative study of five topological invariants of supramolecular chain of different complexes of N-salicylidene-L-valine

L-valine is a crucial amino acid that has rising market demand and numerous uses. It can be used to make specific nutrients, animal feed additives, cosmetic ingredients, and other things in the medical and agricultural fields. N-salicylidene-L-valine (NsLv) is attracting a lot of attention due to its unusual structure and enhanced catalytic and cytotoxic activities. Topological index is a numerical value which is associated with the molecular structure. It is very helpful to predict physio-chemical properties and Quantitative structure-activity relationship and Quantitative structure-property relationship modeling. We study the supramolecular chain (Sc) in the dialkyl tin of complexes 2, 3 and 4 of NsLv to better understand this structure and its topological index-related characteristics. Additionally, we compare topological indices and analyze how these structures relate to one another using concrete examples.