# EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX

Ghalavand, Ali;Ashrafi, Ali Reza;Sharafdini, Reza;Ori, Ottorino

• Accepted : 2019.05.28
• Published : 2019.08.31
• 13 0

#### Abstract

Suppose G is a molecular graph with edge set E(G). The hyper-Zagreb index of G is defined as $HM(G)={\sum}_{uv{\in}E(G)}[deg_G(u)+deg_G(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, all chemical trees of order $n{\geq}12$ with the first twenty smallest hyper-Zagreb index are characterized.

#### Keywords

extremal problems;chemical tree;hyper-Zagreb;graph operation

#### Acknowledgement

Supported by : University of Kashan