Topological Indices of mth Chain Silicate Graphs

Jia-Bao Liu,Syed Sheraz Asghar,Nayab Maryam,Haidar Ali,Muhammad Kashif Shafiq,Asim Naseem

doi:10.3390/math7010042

Abstract

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

Highlights

Introduction and Preliminary ResultsGraph theory is a branch of numerical science in which we apply the apparatuses of the diagram hypothesis to demonstrate the phenomena of compounds scientifically
“A topological index is a quantity that is somehow calculated from the molecular graph and for which we believe that it reflects relevant structural features of the underlying molecule” [1]
The whole theory of topological indices was started by Wiener [3] when he was doing the experiment on the boiling point of paraffin

Summary

Introduction

Introduction and Preliminary ResultsGraph theory is a branch of numerical science in which we apply the apparatuses of the diagram hypothesis to demonstrate the phenomena of compounds scientifically. The degree-based topological indices are very important in chemical graph theory to test the attributes of compounds and drugs, which have been mostly used in chemical and pharmacy engineering [4,5]. In 1975, Milan Randić put forward the topological index, which is based on degree, in his seminar paper [6].

Results

Conclusion