Sharp upper bounds on the spectral radius of the signless Laplacian matrix of a graph

Let G = (V, E) be a simple connected graph. Denote by D(G) the diagonal matrix of its vertex degrees and by A(G) its adjacency matrix. Then the signless Laplacian matrix of G is Q(G) = D(G) + A(G). In this paper, we obtain some new and improved sharp upper bounds on the spectral radius q(1)(G) of the signless Laplacian matrix of a graph G. (C) 2012 Elsevier Inc. All rights reserved.