Hamiltonian Cayley Digraphs on Direct Products of Dihedral Groups


We prove that a Cayley digraph on the direct product of dihedral groups D2n × D2m with outdegree two is Hamiltonian if and only if it is connected.

Share and Cite:

G. Andruchuk, S. Gosselin and Y. Zeng, "Hamiltonian Cayley Digraphs on Direct Products of Dihedral Groups," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 88-92. doi: 10.4236/ojdm.2012.23016.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Curran and J. Gallian, “Hamiltonian Cycles and Paths in Cayley Graphs and Digraphs—A Survey,” Discrete Mathematics, Vol. 156, No. 1-3, 1996, pp. 1-18. doi:10.1016/0012-365X(95)00072-5
[2] J. Gallian and D. Witte, “A Survey: Hamiltonian Cyles in Cayley Graphs,” Discrete Mathematics, Vol. 51, No. 3, 1984, pp. 293-304. doi:10.1016/0012-365X(84)90010-4
[3] K. Kutnar and D. Maru?i?, “Hamilton Cycles and Paths in Vertex-Transitive Graphs—Current Directions,” Dicrete Mathematics, Vol. 309, No. 17, 2009, pp. 5491-5500. doi:10.1016/j.disc.2009.02.017
[4] R. A. Rankin, “A Campanological Problem in Group Theory,” Proceedings of the Cambridge Philosophical Society, Vol. 44, No. 1, 1948, pp. 17-25. doi:10.1017/S030500410002394X
[5] W. Gaschütz, “Zu Einem von B. H. und H. Neumann Gestellten Problem,” Mathematische Nachrichten, Vol. 14, No. 4-6, 1955, pp. 249-252. doi:10.1002/mana.19550140406

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.