Sharp bounds of the zeroth-order general Randić index of bicyclic graphs with given pendent vertices

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• 作者：Xiang-Feng Pan^a ; ^{xfpan@ustc.edu} ; Ning-Ning Lv^b ; ^a ; ^{ningning227@163.com}
• 关键词：Bicyclic graph ; Zeroth-order general Randi&#x107 ; index ; Pendent vertex ; Sharp bound
• 刊名：Discrete Applied Mathematics
• 出版年：2011
• 出版时间：28 February 2011
• 年：2011
• 卷：159
• 期：4
• 页码：240-245
• 全文大小：248 K

文摘

Let G be a simple connected graph and α be a given real number. The zeroth-order general Randić index of ⁰R_α(G) is defined as ∑_vV(G)[d_G(v)]^α, where d_G(v) denotes the degree of the vertex v of G. In this paper, for any α(≠0,1), we give sharp bounds of the zeroth-order general Randić index ⁰R_α of all bicyclic graphs with n vertices and k pendent vertices.