(Generalized) Incidence and Laplacian-Like Energies

Abstract

In this study, for graph $\mathrm{\Gamma }$ with $r$ connected components (also for connected nonbipartite and connected bipartite graphs) and a real number $\epsilon \left(\ne \mathrm{0,1}\right)$ , we found generalized and improved bounds for the sum of $\epsilon$ -th powers of Laplacian and signless Laplacian eigenvalues of $\mathrm{\Gamma }$ . Consequently, we also generalized and improved results on incidence energy $\left(\mathrm{I}\mathrm{E}\right)$ and Laplacian energy-like invariant $\left(\mathrm{L}\mathrm{E}\mathrm{L}\right)$ .