On Laplacian-energy-like invariant of a graph <

Abstract 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 = 1 n - 1 μ i . 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.