Geodesic
On cospectral signed digraphs
Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 191-201.

Voir la notice de l'article provenant de la source Math-Net.Ru

The set of distinct eigenvalues of a signed digraph $S$ together with their respective multiplicities is called its spectrum. Two signed digraphs of same order are said to be cospectral if they have the same spectrum. In this paper, we show the existence of integral, real and Gaussian cospectral signed digraphs. We give a spectral characterization of normal signed digraphs and use it to construct cospectral normal signed digraphs.
Keywords: spectrum of a signed digraph, cospectral signed digraphs, normal signed digraph. 
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M. A. Bhat; T. A. Naikoo; S. Pirzada. On cospectral signed digraphs. Algebra and discrete mathematics, Tome 27 (2019) no. 2, pp. 191-201. http://geodesic.mathdoc.fr/item/ADM_2019_27_2_a3/

[1] B. D. Acharya, “Spectral criterion for the cycle balance in networks”, J. Graph Theory, 4 (1980), 1–11 | DOI | Zbl

[2] B. D. Acharya, M. K. Gill and G. A. Patwardhan, “Quasicospectral graphs and digraphs”, National Symposium on Mathematical Modelling (M.R.I. Allahabad: July), 1982, 19–20

[3] M. Acharya, “Quasi-cospectrality of graphs and digraphs: A creative review”, J. Comb. Inf. Syst. Sci., 37 (2012), 241–256 | Zbl

[4] M. A. Bhat and S. Pirzada, “On equienergetic signed graphs”, Discrete Appl. Math., 189 (2015), 1–7 | DOI | Zbl

[5] D. M. Cvetković, M. Doob and H. Sachs, Spectra of Graphs, Academic press, New York, 1980

[6] F. Esser and F. Harary, “Digraphs with real and Gaussian spectra”, Discrete Appl. Math., 2 (1980), 113–124 | DOI | Zbl

[7] R. A. Horn and C. R. Johnson, Matrix analysis, 2nd ed., Cambridge University Press, Cambridge, 2013 | Zbl

[8] M. H. McAndrew, “On the product of directed graphs”, Proc. Amer. Math. Soc., 14 (1963), 600–606 | DOI | Zbl

[9] S. Pirzada and M. A. Bhat, “Energy of signed digraphs”, Discrete Appl. Math., 169 (2014), 195–205 | DOI | Zbl

[10] J. Rada, “Bounds for the energy of normal digraph”, Linear Multilinear Algebra, 60 (2012), 323–332 | DOI | Zbl