Let G be a simple graph of order n, and let μ 1≥μ 2≥⋯≥μ n=0 be the Laplacian spectrum of G. The Laplacian-energy-like invariant of G (LEL for short) is defined as LEL(G)=∑ i=1n-1√μi. In this paper, a new lower bound for LEL of graphs in terms of the maximum degree is given. Meanwhile, an upper bound and a lower bound for LEL of the line graph (resp., the subdivision graph and the total graph) of a regular graph G are obtained. © 2012 Elsevier Inc. All rights reserved.
Wang, W., & Luo, Y. (2012). On Laplacian-energy-like invariant of a graph. Linear Algebra and Its Applications, 437(2), 713–721. https://doi.org/10.1016/j.laa.2012.03.004