فهرست نشریات علمی دسترسی آزاد ایران

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.