Extremal Laplacian-energy-like invariant of graphs with given matching number

Abstract

Let G be a graph of order n with Laplachian spectrum μ₁ ≥ μ₂ ≥  · · · ≥ μ_n. The Laplacian-energy like invariant of graph G, LEL for short, is defined as: LEL(G) = . In this note, the extremal (maximal and minimal) LEL among all the connected graphs with given matching number is determined. The corresponding extremal graphs are completely characterized with respect to LEL. Moreover a relationship between LEL and the independence number is presented in this note.