Sharp bounds on the zeroth-order general Randić index of unicyclic graphs with given diameter

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• 作者：Xiang-Feng Pan^a ; ^{xfpan@ustc.edu} ; Huiqing Liu^b ; ^{hql_2008@163.com} ; Meimei Liu^c ; ^{a10614043@126.com}
• 关键词：Unicyclic graph ; Zeroth-order general Randi&#x107 ; index ; Diameter ; Sharp bound
• 刊名：Applied Mathematics Letters
• 出版年：2011
• 出版时间：May 2011
• 年：2011
• 卷：24
• 期：5
• 页码：687-691
• 全文大小：253 K

文摘

Let G be a simple connected graph and α be a given real number. The zeroth-order general Randić index 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 work, we give, for any α(≠0,1), some sharp bounds on the zeroth-order general Randić index ⁰R_α of all unicyclic graphs with n vertices and diameter d.