图的Augmented Zagreb 指数的界

Bounds on Augmented Zagreb Index of Graphs

中文关键词:  augmented Zagreb指数  连通图  界

英文关键词:augmented Zagreb index  connected graph  unicyclic graph  bound

中文摘要:

      设$G=(V,E)$是具有$n$个顶点$m$条边的简单连通图,顶点度序列为$\{d_1,d_2,\ldots,d_n\}$. 定义augmented Zagreb指数(简记为AZI)是$AZI=AZI(G)=\sum_{ij\in E}(\frac{d_{i}d_{j}}{d_{i}+d_{j}-2})^{3}$.利用不等式的有关性质我们研究了简单连通图的augmented Zagreb 指数的界,特别对单圈图的augmented Zagreb指数进行了分析,获得了几个有意义的结果.

英文摘要:

      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.