On The Sum of Powers of the Signless Laplacian Eigenvalues of Graphs

Abstract

For a graph $G$ and a real number $\alpha \ne 0$, the graph invariant $s_{\alpha }^{+}(G)$ is the sum of the $\alpha$th power of the non-zero signless Laplacian eigenvalues of $G$. In this paper, several lower and upper bounds for $s_{\alpha }^{+}(G)$ with $\alpha \ne 0,1$ are obtained. Applying these results, we also derive some bounds for the incidence energy of graphs, which generalize and improve on some known results.