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

Abstract

For a simple graph $G$ and a real number $\alpha$ $\left(\alpha \ne 0,1\right)$ 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.