On Computation of Recently Defined Degree-Based Topological Indices of Some Families of Convex Polytopes via M-Polynomial

Deeba Afzal,Mohammad Reza Farahani,Farkhanda Afzal,Samia Ali,Muhammad Javaid

doi:10.1155/2021/5881476

Abstract

Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the topological indices of different structures.

Highlights

Graph theory is a powerful and definable field of mathematics that in every field of science has countless adaptations
Different characteristics of graphs are defined [1]. e topological indices display the graphical structure and many other characteristics in graphs. ey are typically based on the distances between the vertices, on vertex degrees, or on the graph depicted by the matrix
Using the general polynomial is the general method by which we can generate the unique form of topological indices

Summary

Introduction

Graph theory is a powerful and definable field of mathematics that in every field of science has countless adaptations. E topological indices display the graphical structure and many other characteristics in graphs. Using the general polynomial is the general method by which we can generate the unique form of topological indices. M-polynomial [3] that is an algebraic polynomial can explain the behavior of the molecular structure It is graph representative mathematical object which is the most general polynomial developed till and gives us the formulas that are very close to the degree-based topological indices. E M-polynomial introduced in 2015 for a graph G by Emeric Deutsch and Sandi Klavzar [4] is defined as. If we have an M-polynomial of the graph, we can measure its various topological indices. We will calculate closed forms of many degreebased topological indices of some families of convex polytopes by using M-polynomials

Some Families of Convex Polytopes and Their Computational Aspects

M-Polynomial and Topological Indices of Convex Polytopes Tn

M-Polynomial and Topological Indices of Convex Polytopes Sn

Graphical Analysis

Conclusion