Authors: Li, Shuchao
Simić, Slobodan 
Tošič, Dejan
Zhao, Qin
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On ordering bicyclic graphs with respect to the Laplacian spectral radius
Journal: Applied Mathematics Letters
Volume: 24
Issue: 12
First page: 2186
Last page: 2192
Issue Date: 1-Dec-2011
Rank: M21
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.06.023
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) 59815995] 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.
Keywords: Bicyclic graph | Laplacian spectral radius | Spectral ordering
Publisher: Elsevier
Project: Hubei Key Laboratory of Mathematical Sciences, MOE (CCNU09Y01005)
Serbian Ministry for Science (grant 144015G)

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