Sharp Bounds on the Signless Laplacian Spread of Graphs

Abstract

Let G be a connected graph of order n. The signless Laplacian spread of G is defined as \(SQ(G)=q_1(G)-q_n(G)\), where \(q_1(G)\) and \(q_n(G)\) are the maximum and minimum eigenvalues of the signless Laplacian matrix of G, respectively. In this paper, we present some sharp lower bounds for SQ(G) and \(SQ(G)+SQ(G^c)\) in terms of the k-degree and the independence number, respectively.