周后卿.图的Augmented Zagreb 指数的界[J].数学研究及应用,2021,41(1):1~6 |
图的Augmented Zagreb 指数的界 |
Bounds on Augmented Zagreb Index of Graphs |
投稿时间:2020-02-20 修订日期:2020-09-27 |
DOI:10.3770/j.issn:2095-2651.2021.01.001 |
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 |
基金项目:国家自然科学基金(Grant No.61672356),邵阳学院教学改革研究项目(Grant No.2017JG19). |
|
摘要点击次数: 743 |
全文下载次数: 597 |
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. |
查看全文 查看/发表评论 下载PDF阅读器 |