Generalization for the Average Value of the Difference Between the Energies of Two Graphs

Let (G) over cap (n,m) denote the set of all simple graphs with n vertices and m edges. In this paper, for a given type of graph Hermite matrix A, we determine the average values of the difference between A-energies of two graphs randomly chosen from (G) over cap (n,m). These results yield criterions for deciding when two graphs are almost A-equienergetic. Our results generalize some previous results in the literature. Moreover, we give new results on Laplacian energy.