Bounds of Zagreb indices and hyper Zagreb indices

Abstract

The hyper Zagreb index is a kind of extensions of Zagreb index, used for predicting physicochemical properties of organic compounds. Given a graph $G=(V(G),E(G))$, the first hyper-Zagreb index is the sum of the square of edge degree over edge set $E(G)$ and defined as $H{M}_1(G)={\sum }_{e=uv\in E(G)}d(e{)}^2$, where $d(e)=d(u)+d(v)$ is the edge degree. In this work we define the second hyper-Zagreb index on the adjacent edges as $H{M}_2(G)={\sum }_{e\sim f}d(e)d(f)$, where $e\sim f$ represents the adjacent edges of $G$. By inequalities, we explore some upper and lower bounds of these hyper-Zagreb indices, and provide the relation between Zagreb indices and hyper Zagreb indices.

Accepted by Mathematical Reports

Cited by in corpus (1)

• F-index of graphs based on new operations related to the join of graphs