Topological Indices of Certain Transformed Chemical Structures

Symmetry

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

Journal of Computational and Theoretical Nanoscience, 2016

In QSAR/QSPR study, topological indices such as Shultz index, generalized Randic index, Zagreb index, general sum-connectivity index, atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are utilized to guess the bioactivity of chemical compounds. A topological index in fact relates a chemical structure with a numeric number. Graph theory has established a significant use in this area of research. In this paper we computed ABC 4 and GA 5 indices of the line graph of tadpole, wheel and ladder graphs using the notion of subdivision.

International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022

The application of topology in molecular graph and drug design is covered in this article. On the basis of the most recent developments in this area, an overview of the use of topological indices (TIs) in the process of drug design and development is provided. The introduction of concepts used in drug design and discovery, graph theory, and topological indices is the primary goal of the first section of this book. Researchers can learn more about the physical characteristics, chemical reactivity, and biological activity of these chemical molecular structures by using topological indices. In order to compensate for the lack of chemical experiments and offer a theoretical foundation for the production of medications and chemical materials, topological indices on the chemical structure of chemical materials and drugs are studied. In this article, we concentrate on the family of smart polymers that are frequently utilised in the production of drugs.

Scientific Reports, 2023

A numeric quantity that characterizes the whole structure of a network is called a topological index. In the studies of QSAR and QSPR, the topological indices are utilized to predict the physical features related to the bioactivities and chemical reactivity in certain networks. Materials for 2D nanotubes have extraordinary chemical, mechanical, and physical capabilities. They are extremely thin nanomaterials with excellent chemical functionality and anisotropy. Since, 2D materials have the largest surface area and are the thinnest of all known materials, they are ideal for all applications that call for intense surface interactions on a small scale. In this paper, we derived closed formulae for some important neighborhood based irregular topological indices of the 2D nanotubes. Based on the obtained numerical values, a comparative analysis of these computed indices is also performed. Carbon nanotubes (CNTs) are actually cylindrical molecules that comprise of rolled-up sheets of single-layer carbon atoms (graphene). They can be single-walled having a less than 1 nm (nm) diameter or multi-walled, comprising of numerous concentrically interlinked nanotubes, with around more than 100 nm diameters. Sumio Iijima discovered the multi-walled carbon nanotubes in 1991 1. CNTs are bonded with sp 2 bonds chemically, an extremely strong form of molecular interaction. These nanotubes inherit electrical properties from graphene, which are determined by the rolling-up direction of the graphene layers. Apart from these, CNTs also have distinctive mechanical and thermal properties like lightweight , high tensile strength, low density, better thermal conductivity, high aspect ratio and high chemical stability. All these properties make them intriguing for new materials development, especially CNTs are best candidates for hydrogen storage cells, cathode ray tubes (CRTs), electronic devices, electron field emitters and transistors. Keeping in view their strong applicability and importance, it is very important to model and characterize these CNTs for a better understanding of their structural topology for enhancement of their physical properties. The study of chemicals using a mathematical method is called mathematical chemistry. Chemical graph theory is a branch of chemistry that uses graph theory concepts to convert chemical events into mathematical models. The chemical graph is a simple connected graph in which atoms and chemical bonds are taken as vertices and edges respectively. A connected graph of order n = |V (G)| and size m = |E(G)| can be created with the help of G and edge set E. The focus of research in the area of nanotechnology is on atoms and Molecules. The Cartesian product of a path graph of m and n is called a 2D lattice. Graph theory has emerged as a powerful tool for analyzing the structural properties of complex systems represented by graphs. Topological indices, which are numerical quantities derived from graph theory 2-8 , have gained significant attention due to their ability to concisely capture important graph properties. Degree-based topological indices specifically utilize the degrees of vertices in a graph to quantify its structural characteristics 9. Degree based indices, such as the Randić index, the atom-bond connectivity index, and the Harary index, capture the connectivity and branching patterns in a graph by considering the distances between pairs of vertices in relation to their degrees 10-14. These indices have found wide applications in drug design, chemical graph theory, and network analysis 15-18 .

Journal of Molecular Structure-theochem, 1997

Topics in Current Chemistry, 1983

Chapter 1. On the Complexity of Fullerenes and Nanotubes

In this research study, several topological indices have been investigated for linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori. The calculated indices are first, second, third and modified second Zagreb indices. In addition, the first and second Zagreb coindices of these nanostructures were calculated. The explicit formulae for connectivity indices of various families of Tetracenic nanotubes and nanotori are presented in this manuscript. These formulae correlate the chemical structure of nanostructures to the information about their physical features.

In this paper, several topological indices are investigated for H-Phenylenic nanotube, H-Naphthylenic nanotube and H-Anthracenic nanotube. The calculated indices are product-connectivity index, sum-connectivity index, geometric-arithmetic index and atom-bond connectivity index.

Discrete & Continuous Dynamical Systems - S

Topological indices defined on molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. Thus, the study of the topological indices on chemical structure of chemical materials and drugs can make up for lack of chemical experiments and can provide a theoretical basis for the manufacturing of drugs and chemical materials. In this paper, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing. In chemical graph theory, a topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds e.g., boiling point and melting point. More preciously, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing, and computed exact results for degree based topological indices.

Journal of Chemical Information and Computer Sciences, 2004

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type EState index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type EState indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.