# EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX

• Ghalavand, Ali (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan) ;
• Ashrafi, Ali Reza (Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan) ;
• Sharafdini, Reza (Department of Mathematics, Faculty of Science, Persian Gulf University) ;
• Ori, Ottorino (Actinum Chemical Research)
• Accepted : 2019.05.28
• Published : 2019.08.31
• 54 8

#### 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

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