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A sharp upper bound on the signless Laplacian spectral radius of graphs

Authors:	Shu-Yu Cui Gui-Xian Tian Jing-Jing Guo

Institution:	1. Xingzhi College, Zhejiang Normal University, Jinhua, Zhejiang, 321004, PR China;2. College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, PR China

Abstract:	Let G be a simple connected graph of order n with degree sequence _d₁,_d₂,…,_d_n $d_{1}, d_{2}, \dots, d_{n}$ in non-increasing order. The signless Laplacian spectral radius ρ(Q(G)) $ρ (Q (G))$ of G is the largest eigenvalue of its signless Laplacian matrix Q(G) $Q (G)$ . In this paper, we give a sharp upper bound on the signless Laplacian spectral radius ρ(Q(G)) $ρ (Q (G))$ in terms of _d_i $d_{i}$ , which improves and generalizes some known results.

Keywords:	05C35 05C50 05C90
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