On Laplacian-energy-like invariant and incidence energy

For a simple connected graph G with n-vertices having Laplacian eigenvalues‎ ‎\mu_۱‎, ‎\mu_۲‎, ‎\dots‎, ‎\mu_{n-۱}‎, ‎\mu_n=۰‎, ‎and signless Laplacian eigenvalues q_۱‎, ‎q_۲,\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=۱}^{n-۱}\sqrt{\mu_i} and IE(G)=\sum_{i=۱}^{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.

Keywords:

Spectra of graph , energy of graph , Laplacian energy , incidence energy