Bounds on Augmented Zagreb Index of Graphs
Received:February 20, 2020  Revised:September 27, 2020
Key Word: augmented Zagreb index   connected graph   unicyclic graph   bound
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.61672356) and the Teaching Reform Research Project of Shaoyang University (Grant No.2017JG19).
 Author Name Affiliation Houqing ZHOU Department of Mathematics, Shaoyang University, Hunan 422000, P. R. China
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Let $G=(V,E)$ be a simple connected graph with $n~(n\geq 3)$ vertices and $m$ edges, with vertex degree sequence $\{d_{1}, d_{2},\ldots, d_{n}\}$. The augmented Zagreb index is defined as $AZI=AZI(G)=\sum_{ij\in E}(\frac{d_{i}d_{j}}{d_{i}+d_{j}-2})^{3}$. Using the properties of inequality, we investigate the bounds of $AZI$ for connected graphs, in particular unicyclic graphs in this paper, some useful conclusions are obtained.