A lower bound for the spectral radius of graphs with fixed diameter

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• 作者：Sebastian M. Cioabă ; Edwin R. van Dam ; Jack H. Koolen ; Jae-Ho Lee
• 刊名：European Journal of Combinatorics
• 出版年：2010
• 出版时间：August 2010
• 年：2010
• 卷：31
• 期：6
• 页码：1560-1566
• 全文大小：256 K

文摘

We determine a lower bound for the spectral radius of a graph in terms of the number of vertices and the diameter of the graph. For the specific case of graphs with diameter three we give a slightly better bound. We also construct families of graphs with small spectral radius, thus obtaining asymptotic results showing that the bound is of the right order. We also relate these results to the extremal degree/diameter problem.