On Laplacian-energy-like invariant of a graph

Let G be a simple graph of order n, and let μ1≥μ2≥⋯≥μn=0 be the Laplacian spectrum of G. The Laplacian-energy-like invariant of G (LEL for short) is defined as . 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.