Vertex-Degree Based Topological Indices of Graphene

Abstract

A vertex-degree-based (VDB, for short) topological index is defined for a graph G with n vertices as where is the number of edges of G joining a vertex of degree i with a vertex of degree j, and is a set of real numbers. In this paper, we present a general formula to calculate VDB topological indices of graphene systems. As a byproduct, we solve the following extremal value problem: given a VDB topological index find the graphene with maximal value of and the graphene with minimal value of among all graphene with h hexagons.