Asymptotic results on the spectral radius and the diameter of graphs

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• 作者：Sebastian M. Cioabă ; Edwin R. van Dam ; Jack H. Koolen ; Jae-Ho Lee
• 关键词：Graphs ; Spectral radius ; Diameter ; Limit points ; Quipus ; href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4XHJXCN-2&_mathId=mml3&_user=10&_cdi=5653&_pii=S0024379509004911&_rdoc=21&_issn=00243795&_acct=C0
• 刊名：Linear Algebra and its Applications
• 出版年：2010
• 出版时间：15 January 2010
• 年：2010
• 卷：432
• 期：2-3
• 页码：722-737
• 全文大小：246 K

文摘

We study graphs with spectral radius at most and refine results by Woo and Neumaier [R. Woo, A. Neumaier, On graphs whose spectral radius is bounded by , Graphs Combinatorics 23 (2007) 713–726]. We study the limit points of the spectral radii of certain families of graphs, and apply the results to the problem of minimizing the spectral radius among the graphs with a given number of vertices and diameter. In particular, we consider the cases when the diameter is about half the number of vertices, and when the diameter is near the number of vertices. We prove certain instances of a conjecture posed by Van Dam and Kooij [E. R. Van Dam, R. E. Kooij, The minimal spectral radius of graphs with a given diameter, Linear Algebra Appl. 423 (2007) 408–419] and show that the conjecture is false for the other instances.