On the Laplacian-Energy-Like Invariant of Graphs

Abstract

The Laplacian-energy-like graph invariant of a graph \(G\), denoted by \(LEL(G)\), is defined as \(LEL(G) = \sum\limits_{i=1}^{n} \sqrt{\mu_i}\), where \(\mu_i\) are the Laplacian eigenvalues of graph \(G\). In this paper, we study the maximum \(LEL\) among graphs with a given number of vertices and matching number. Some results on \(LEL(G)\) and \(LEL(\overline{G})\) are obtained.