Naslov (eng)

Some Spectral Characterizations of Equienergetic Regular Graphs and Their Complements

Autor

Jovanović, Irena M.
Zogić, Emir

Opis (eng)

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.

Jezik

engleski

Datum

2021

Licenca

© All rights reserved

Predmet

Keywords: Graph spectrum, equienergetic graphs, regular graphs

Deo kolekcije (1)

o:28516

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