Bian He, Ya-Lei Jin, Xiao-Dong Zhang
Published 2012-09-14Version 1
In this paper, we present a sharp upper and lower bounds for the signless Laplacian spectral radius of graphs in terms of clique number. Moreover, the extremal graphs which attain the upper and lower bounds are characterized. In addition, these results disprove the two conjectures on the signless Laplacian spectral radius in [P. Hansen and C. Lucas, Bounds and conjectures for the signless Laplacian index of graphs, Linear Algebra Appl., 432(2010) 3319-3336].
Comments: 15 pages 1 figure; linear algebra and its applications 2013
Connectivity and eigenvalues of graphs with given girth or clique number
The Algebraic Connectivity and the Clique Number of Graphs
A (forgotten) upper bound for the spectral radius of a graph
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