On the Laplacian-energy-like invariant

Abstract

Let G be a connected graph of order n with Laplacian eigenvalues μ1≥μ2≥⋯≥μn-1> μn=0. The Laplacian-energy-like invariant of the graph G is defined as LEL = LEL(G)= Σi=1n-1√μi. Lower and upper bounds for LEL are obtained, in terms of n, number of edges, maximum vertex degree, and number of spanning trees. © 2013 Elsevier Inc. All rights reserved.