Bounds For Incidence Energy Of Graphs

Let G be a graph with n vertices, the incidence energy of G, denoted by IE(G), is defined as IE (G) is the signless Laplacian eigenvalues of G. The graph invariant sα (G) is equal to the sum of a-th powers of signless Laplacian eigenvalues of G. In this paper, we obtain bounds for incidence energy of some graphs. First, we give upper bounds for incidence energy in terms of n, m, maximum degree, minimum degree, and the first Zagreb index. Next, we obtain some bounds for sα (G) of connected graphs. These results yield, as immediate special cases, bounds for the incidence energy.