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On ordering bicyclic graphs with respect to the Laplacian spectral radius

✍ Scribed by Shuchao Li; Slobodan K. Simić; Dejan V. Tošić; Qin Zhao

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
303 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

A connected graph of order n is bicyclic if it has n + 1 edges. He et al. [C.X. He, J.Y. Shao, J.L. He, On the Laplacian spectral radii of bicyclic graphs, Discrete Math. 308 (2008) 5981-5995] determined, among the n-vertex bicyclic graphs, the first four largest Laplacian spectral radii together with the corresponding graphs (six in total). It turns that all these graphs have the spectral radius greater than n -1. In this paper, we first identify the remaining n-vertex bicyclic graphs (five in total) whose Laplacian spectral radius is greater than or equal to n -1. The complete ordering of all eleven graphs in question was obtained by determining the next four largest Laplacian spectral radii together with the corresponding graphs.

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