On the Hyper Zagreb index of certain generalized thorn graphs

TL;DR

This paper calculates the hyper Zagreb index for specific generalized thorn graphs, providing formulas and insights into how this topological index behaves in these graph classes.

Contribution

It introduces formulas for the hyper Zagreb index of certain generalized thorn graphs, expanding understanding of this index in complex graph structures.

Findings

Derived explicit formulas for the hyper Zagreb index of generalized thorn graphs.

Provided theoretical insights into the behavior of the hyper Zagreb index in these graphs.

Enhanced the mathematical understanding of topological indices in graph theory.

Abstract

Let $G=(V,E)$ be a graph with $n$ vertices and $m$ edges. The hyper Zagreb index of $G$, denoted by $HM(G)$, is defined as $HM(G) =\sum\limits_{uv \in E(G)}\left[d_{G}(u)+d_G(v)\right]^{2}$ where $d_G(v)$ denotes the degree of a vertex $v$ in $G$. In this paper we compute the hyper Zagreb index of certain generalized thorn graphs.