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

Abstract

Let G 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 . 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.

Keywords

• (A-) energy of graph,almost (A-) equienergetic graphs

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