Harary Energy, Complementary Distance Energy and Equienergetic Graphs

Abstract

The energy of a graph G is defined as the absolute sumof its eigenvalues. Numerous studies have focused on similar aspectsof graph energy, including Harary energy, distance energy, complemen-tary distance energy, and Laplacian energy. However, relatively fewinvestigations have addressed the class of graphs of the same order thatexhibit equienergetic properties with respect to more than two associ-ated matrices. In this paper, we characterize a class of graphs that shareequienergetic attributes with respect to adjacency, Harary, and comple-mentary distance matrices. Additionally, we present a large class ofgraphs demonstrating equienergetic attributes concerning four matricesassociated with graphs of the same order.