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

For a graph \( G \) and a real number \( \alpha \neq 0 \), 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 \( \alpha \neq 0, 1 \) are obtained. Applying these results, we also derive some bounds for the incidence energy of graphs, which generalize and improve on some known results.