Sharp Bounds for the Signless Laplacian Spectral Radius in Terms of   Clique Number
  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]. 
Bian He, Ya-Lei Jin and Xiao-Dong Zhang
math.CO