Some new bounds for the signless Laplacian energy of a graph

Abstract

For a simple graph G with n vertices, m edges and signless Laplacian eigen-n is the average vertex degree of G. In this paper, we obtain two lower bounds ( see Theorem 3.1 and Theorem 3.2 ) and one upper bound for QE(G) ( see Theorem 3.3 ), which improve some known bounds of QE(G), and moreover, we determine the corresponding extremal graphs that achieve our bounds. By subproduct, we also get some bounds for QE(G) of regular graph G.