Unicyclic and bicyclic graphs with minimal augmented Zagreb index

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• 作者：Fuqin Zhan ; Youfu Qiao ; Junliang Cai
• 关键词：05C35 ; 05C75 ; 92E10 ; augmented Zagreb index ; extremal graphs ; unicyclic graphs ; bicyclic graphs
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,303 KB
• 参考文献：1. Harary, F (1969) Graph Theory. Addison-Wesley, Reading
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• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

The augmented Zagreb index of a graph G is defined as $$ \operatorname{AZI}(G)=\sum_{uv\in E(G)} \biggl( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2} \biggr)^{3}, $$ where \(E(G)\) is the edge set, and \(d_{u}\) , \(d_{v}\) are the degrees of vertices u and v in G, respectively. This new molecular structure descriptor, introduced by Furtula et al. (J.?Math. Chem. 48:370-380, 2010), has proven to be a valuable predictive index in the study of the heat of formation in heptanes and octanes. In this paper, the n-vertex unicyclic graphs with the minimal and the second minimal AZI indices and the n-vertex bicyclic graphs with the minimal AZI index are determined.