Note on the Sum of Powers of Signless Laplacian Eigenvalues of Graphs

Abstract

For a simple graph $G$ and a real number $\alpha $ $\left(\alpha \neq 0,1\right) $ the graph invariant $s_{\alpha}\left(G\right) $ is equal to the sum of powers of signless Laplacian eigenvalues of $G$. In this note, we present some new bounds on $s_{\alpha}\left(G\right) $. As a result of these bounds, we also give some results on incidence energy.