On the Randi? Index of Unicyclic Conjugated Molecules

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• 作者：Huiqing Liu ; Xiangfeng Pan and Jun-Ming Xu
• 关键词：Randić ; index ; unicyclic graph ; given size of matching
• 刊名：Journal of Mathematical Chemistry
• 出版年：2006
• 出版时间：August, 2006
• 年：2006
• 卷：40
• 期：2
• 页码：135-143
• 全文大小：138 KB

文摘

The Randić index R(G) of a graph G is the sum of the weights(d(u)d(v))-\frac12(d(u)d(v))^{-\frac{1}{2}} of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we first present a sharp lower bound on the Randić index of conjugated unicyclic graphs (unicyclic graphs with perfect matching). Also a sharp lower bound on the Randić index of unicyclic graphs is given in terms of the order and given size of matching.