Igor Milovanovic - Faculty of Electronic Engineering
M. Matejic - University of Nis, Serbia
P. Milosevic - University of Nis, Serbia
Emina Milovanovic - Faculty of Electronic Engineering
Akbar Ali - University of Management and Technology, Sialkot, Pakistan

‎‎‎For a simple connected graph $G$ of order $n$ and size $m$‎, ‎the Laplacian energy of $G$ is defined as‎ ‎$LE(G)=\sum_{i=۱}^n|\mu_i-\frac{۲m}{n}|$ where $\mu_۱‎, ‎\mu_۲,\ldots‎,‎‎\mu_{n-۱}‎, ‎\mu_{n}$‎ ‎are the Laplacian eigenvalues of $G$ satisfying $\mu_۱\ge \mu_۲\ge\cdots \ge \mu_{n-۱}>‎ ‎\mu_{n}=۰$‎. ‎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 $LE(G)$‎.

‎Laplacian eigenvalue‎, ‎Laplacian energy (of a‎ ‎graph)‎, ‎first Zagreb index