On Laplacian energy in terms of graph invariants

For C being a graph with ti vertices and T11 edges, and with Laplacian eigenvalues mu(1) >= mu(2) >= ... >= mu(n-1) >= mu(n) - 0the Laplacian energy is defined as LE - Sigma(n)(i=1)vertical bar mu(i) - 2 mu/n. Let ci be the largest positive integer such that mu(sigma) >= 2 mu/n. We characterize the graphs satisfying sigma = n - 1. Using this, we obtain lower bounds for LE in terms of n, in, and the first Zagreb index. In addition, we present some upper bounds for LE in terms of graph invariants such as n, maximum degree, vertex cover number, and spanning tree packing number. (C) 2015 Elsevier Inc. All rights reserved.