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Nonderogatory unicyclic digraphs. (English) Zbl 1139.05026
Summary: A digraph is nonderogatory if its characteristic polynomial and minimal polynomial are equal. We find a characterization of nonderogatory unicyclic digraphs in terms of Hamiltonicity conditions. An immediate consequence of this characterization ia that the complete product of difans and diwheels is nonderogatory.

MSC:
05C20Directed graphs (digraphs), tournaments
WorldCat.org
Full Text: DOI EuDML
References:
[1] A. Mowshowitz, “Graphs, groups and matrices,” in Proceedings of the 25th Summer Meeting of the Canadian Mathematical Congress, pp. 509-522, Lakehead University, Thunder Bay, Ont, Canada, 1971. · Zbl 0323.05117
[2] D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs, vol. 87 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1980. · Zbl 0458.05042
[3] C. S. Gan and V. C. Koo, “On annihilating uniqueness of directed windmills,” in Proceedings of the 7th Asian Technology Conference in Mathematics (ATCM ’02), Melaka, Malaysia, December 2002.
[4] C. S. Gan, “The complete product of annihilatingly unique digraphs,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 9, pp. 1327-1331, 2005. · Zbl 1076.05040 · doi:10.1155/IJMMS.2005.1327 · eudml:51822
[5] K. S. Lam, On digraphs with unique annihilating polynomial, Ph.D. thesis, University of Malaya, Kuala Lumpur, Malaysia, 1990.
[6] C.-K. Lim and K. S. Lam, “The characteristic polynomial of ladder digraph and an annihilating uniqueness theorem,” Discrete Mathematics, vol. 151, no. 1-3, pp. 161-167, 1996. · Zbl 0853.05055 · doi:10.1016/0012-365X(94)00093-X
[7] J. Rada, “Non-derogatory directed windmills,” in preparation.
[8] D. Bravo and J. Rada, “Coalescence of difans and diwheels,” to appear in Bulletin of the Malaysian Mathematical Sciences Society. · Zbl 1141.05048