Relations Between Vertex–Edge Degree Based Topological Indices and Mve-Polynomial of r−Regular Simple Graph

Abstract

One of the more exciting polynomials among the newly presented graph algebraic polynomials is the M−Polynomial, which is a standard method for calculating degree−based topological indices. In this paper, we define the Mve−polynomials based on vertex edge degree and derive various vertex–edge degree based topological indices from them. Thus, for any graph, we provide some relationships between vertex–edge degree topological indices. Also, we discuss the general Mve−polynomial of r−regular simple graph. Finally, we computed the Mve−polynomial of the 2−ary tree graph.