On Laplacian energy in terms of graph invariants

Abstract

© 2015 Elsevier Inc. Abstract For G being a graph with n vertices and m edges, and with Laplacian eigenvalues ^μ1≥^μ2≥⋯≥μn-<inf>1</inf>≥^μn=0, the Laplacian energy is defined as LE=Σi=1n|^μi-2m/n|. Let σ be the largest positive integer such that μ<inf>σ</inf> ≥ 2m/n. We characterize the graphs satisfying σ=n-1. Using this, we obtain lower bounds for LE in terms of n, m, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, m, maximum degree, vertex cover number, and spanning tree packing number.