Abstract: The energy E(G) of a graph G is defined as E(G) = ∑|λi(G)|, where λi(G),for i = 1, 2, . . . , n, are the adjacency eigenvalues of G. Two graphs with the same number of vertices are said to be equienergetic if they have the same energy. The spectral distance σ(G1, G2) of two non-isomorphic graphs G1 and G2 of order n, is σ(G1, G2) = ∑ |λi(G1) − λi(G2)|. In [H. S. Ramane, B. Parvathalu, D. D. Patil, K. Ashoka, Graphs Equienergetic with Their Complements, MATCH Commun. Math. Comput. Chem. 82 (2019) 471–480], the authors asked about spectral properties of graphs which are equienergetic with their complements. Using spectral distances of graphs, we give a necessary and sufficient condition for a regular graph to have the energy equal to the energy of its complement. Based on this result, strongly regular graphs equienergetic with their complements are characterized. A spectral property that two equienergetic regular graphs should possess in order for their complements to have equal energies is stated. Equienergetic regular graphs with respect to some graph operations are considered by spectral means, as well. https://phaidrabg.bg.ac.rs/o:28907 ISSN: 0340-6253 2021 info:eu-repo/semantics/article Keywords: Graph spectrum, equienergetic graphs, regular graphs eng application/pdf 407611 bytes All rights reserved Some Spectral Characterizations of Equienergetic Regular Graphs and Their Complements MATCH Communications in Mathematical and in Computer Chemistry 86(3) Jovanović, Irena M. Zogić, Emir