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Sharp Bounds for the Signless Laplacian Spectral Radius in Terms of Clique Number

Published 14 Sep 2012 in math.CO | (1209.3214v1)

Abstract: 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].

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