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On the signless Laplacian spectral radius of graphs with cut vertices

✍ Scribed by Bao-Xuan Zhu

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 129 KB
Volume: 433
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.04.041

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✦ Synopsis

In this paper, we show that among all the connected graphs with n vertices and k cut vertices, the maximal signless Laplacian spectral radius is attained uniquely at the graph G n,k , where G n,k is obtained from the complete graph K n-k by attaching paths of almost equal lengths to all vertices of K n-k . We also give a new proof of the analogous result for the spectral radius of the connected graphs with n vertices and k cut vertices (see [A. Berman, X.-D. Zhang, On the spectral radius of graphs with cut vertices, J. Combin. Theory Ser. B 83 (2001) 233-240]). Finally, we discuss the limit point of the maximal signless Laplacian spectral radius.

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