University of Isfahan Transactions on Combinatorics 2251-8657 4 3 2015 09 01 On Laplacian-energy-like invariant and incidence energy 25 35 7581 10.22108/toc.2015.7581 EN Shariefuddin Pirzada University of Kashmir Hilal A. Ganie University of Kashmir Journal Article 2014 12 04 For a simple connected graph $G$ with $n$-vertices having Laplacian eigenvalues‎ ‎$\mu_1$‎, ‎$\mu_2$‎, ‎$\dots$‎, ‎$\mu_{n-1}$‎, ‎$\mu_n=0$‎, ‎and signless Laplacian eigenvalues $q_1‎, ‎q_2,\dots‎, ‎q_n$‎, ‎the Laplacian-energy-like invariant($LEL$) and the incidence energy ($IE$) of a graph $G$ are respectively defined as $LEL(G)=\sum_{i=1}^{n-1}\sqrt{\mu_i}$ and $IE(G)=\sum_{i=1}^{n}\sqrt{q_i}$‎. ‎In this paper‎, ‎we obtain some sharp lower and upper bounds for the Laplacian-energy-like invariant and incidence energy of a graph‎. https://toc.ui.ac.ir/article_7581_bda8b11c9a6008d79291140ecbdc3be6.pdf