University of Isfahan Transactions on Combinatorics 2251-8657 8 2 2019 06 01 A note on some lower bounds of the Laplacian energy of a graph 13 19 23370 10.22108/toc.2019.115269.1616 EN Igor Z. Milovanovic Faculty of Electronic Engineering M. Matejic University of Nis, Serbia P. Milosevic University of Nis, Serbia Emina I. Milovanovic Faculty of Electronic Engineering Akbar Ali University of Management and Technology, Sialkot, Pakistan Journal Article 2019 01 23 ‎‎‎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 $\mu_1\ge \mu_2\ge\cdots \ge \mu_{n-1}>‎ ‎\mu_{n}=0$‎. ‎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 $LE(G)$‎. https://toc.ui.ac.ir/article_23370_6285b197572578fd5d6ac1d563c9ba16.pdf