A note on some lower bounds of the Laplacian energy of a graph

Abstract

‎‎‎For a simple connected graph $G$ of order $n$ and size $m$‎, ‎the Laplacian energy of $G$ is defined as‎ ‎$LE(G)=sum_{i=1}^n|mu_i-frac{2m}{n}|$ where $mu_1‎, ‎mu_2,ldots‎,‎‎mu_{n-1}‎, ‎mu_{n}$‎ ‎are the Laplacian eigenvalues of $G$ satisfying $mu_1ge mu_2gecdots ge mu_{n-1}>‎ ‎mu_{n}=0$‎. ‎In this note‎, ‎some new lower bounds on the graph invariant $LE(G)$ are derived‎. ‎The obtained results are compared with some already known lower bounds of $LE(G)$‎.