A Generalization of the Incidence Energy and the Laplacian-Energy-Like Invariant

For a graph G and a real number alpha, the graph invariant s(alpha)(G) is the sum of the alpha th powers of the signless Laplacian eigenvalues and sigma(alpha)(G) is the sum of the alpha th powers of the Laplacian eigenvalues of G. In this study, for appropriate vales of alpha, we give some bounds for the generalized versions of incidence energy and of the Laplacian-energy-like invariant of graphs.