Vertex-Degree Based Topological Indices of Graphene

Abstract

A vertex-degree-based (VDB, for short) topological index $\phi$ is defined for a graph G with n vertices as

$\phi (G)=\sum _{1\le i\le j\le n-1}{m}_{i,j}(G)\phi (i,j),$

where $m_{i,j}=m_{i,j}(G)$ is the number of edges of G joining a vertex of degree i with a vertex of degree j, and $\left\{\phi (i,j)\right\}$ 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 $\phi ,$ find the graphene with maximal value of $\phi$ and the graphene with minimal value of $\phi ,$ among all graphene with h hexagons.

Keywords:

• Benzenoid system
• extremal value
• graphene
• VDB topological index

Declaration of interest

There are no conflicts of interest.