New Bounds on the Incidence Energy, Randic Energy and Randic Estrada Index

For a simple graph G and a real number alpha (not equal 0,1) the graph invariant s(alpha) is equal to the sum of powers of signless Laplacian eigenvalues of G. In this paper, we present some new bounds on s(alpha) of graphs and improve some results which was obtained on bipartite graphs. As a result of these bounds, we also obtain the some improved results on incidence energy. In addition, we study on Randic energy (RE) and Randic Estrada index (REE) of (bipartite) graphs.