Complete solution to a conjecture on Randić index

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• 作者：Xueliang Li ; Bolian Liu ; Jianxi Liu
• 关键词：Simple graph ; Minimum degree ; Randić ; index ; Minimum value
• 刊名：European Journal of Operational Research
• 出版年：2010
• 出版时间：1 January 2010
• 年：2010
• 卷：200
• 期：1
• 页码：9-13
• 全文大小：245 K

文摘

For a graph G, the Randić index R(G) of G is defined by , where d(u) is the degree of a vertex u and the summation runs over all edges uv of G. Let G(k,n) be the set of connected simple graphs of order n with minimum degree k. Bollobás and Erdős once asked for finding the minimum value of the Randić index among the graphs in G(k,n). There have been many partial solutions for this question. In this paper we give a complete solution to the question.