Computing Topological Indices and Polynomials for Line Graphs

Shahid Imran,Muhammad Nadeem,Muhammad Imran,Muhammad Siddiqui

doi:10.3390/math6080137

Abstract

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point, solidness, strain vitality, and so forth, of synthetic mixes. The idea of the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials was set up in the substance diagram hypothesis in light of vertex degrees. These indices are valuable in the investigation of calming exercises of certain compound systems. In this paper, we computed the first and second Zagreb index, the hyper Zagreb index, multiple Zagreb indices and Zagreb polynomials of the line graph of wheel and ladder graphs by utilizing the idea of subdivision.

Highlights

Chemical graph theory is a branch of mathematical chemistry in which we apply apparatuses of the graph hypothesis to display the substance numerically
A topological index is a numerical amount related to the concoction constitution indicating the connection of the substance structure with numerous physio-synthetic properties, compound reactivity, and organic action
In 2011, Ranjini et al figured the unequivocal articulations for the Schultz lists of the subdivision diagrams of the tadpole, wheel, steerage, and stepping stool charts

Summary

Introduction

Chemical graph theory is a branch of mathematical chemistry in which we apply apparatuses of the graph hypothesis to display the substance numerically. This hypothesis contributes noticeably to the synthetic sciences. A sub-atomic diagram is a straightforward limited graph in which vertices mean that the atoms and edges indicate concoction bonds in hidden compound structure. A topological index is a numerical amount related to the concoction constitution indicating the connection of the substance structure with numerous physio-synthetic properties, compound reactivity, and organic action. Mathematics 2018, 6, 137 done by Wiener [1], while at the same time, he was aiming to determine the breaking point of paraffin He named this list as the way number. See [7,8,9] for details

Applications of Topological Indices

Conclusions