A Note on Hamiltonian Circulant Digraphs of Outdegree Three

ABSTRACT

We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work of Miklavi and ?parl, who previously deter-mined the Hamiltonicity of these digraphs in the case where and , to other values of which depend on the generators and .

We construct Hamilton cycles in connected loopless circulant digraphs of outdegree three with connection set of the form for an integer satisfying the condition for some integer such that , where . This extends work of Miklavi and ?parl, who previously deter-mined the Hamiltonicity of these digraphs in the case where and , to other values of which depend on the generators and .

Cite this paper

G. Andruchuk and S. Gosselin, "A Note on Hamiltonian Circulant Digraphs of Outdegree Three,"*Open Journal of Discrete Mathematics*, Vol. 2 No. 4, 2012, pp. 160-163. doi: 10.4236/ojdm.2012.24032.

G. Andruchuk and S. Gosselin, "A Note on Hamiltonian Circulant Digraphs of Outdegree Three,"

References

[1] R. A. Rankin, “A Campanological Problem in Group Theory,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 44, No. 1, 1948, pp. 17-25. doi:10.1017/S030500410002394X

[2] S. C. Locke and D. Witte, “On Non-Hamiltonian Circulant Digraphs of Outdegree Three,” Journal of Graph Theory, Vol. 30, No. 4, 1999, pp. 319-331. doi:10.1002/(SICI)1097-0118(199904)30:4<319::AID-JGT6>3.0.CO;2-1

[3] D. Witte Morris, J. Morris and K. Webb, “Hamiltonian Cycles in (2,3,c)-Circulant Digraphs,” Discrete Mathematics, Vol. 309, No. 17, 2009, pp. 5484-5490. doi:10.1016/j.disc.2009.01.001

[4] ?. Miklavi and P. ?parl, “On Hamiltonicity of Circulant Digraphs of Outdegree Three,” Discrete Mathematics, Vol. 309, No. 17, 2009, pp. 5437-5443. doi:10.1016/j.disc.2008.12.004

[1] R. A. Rankin, “A Campanological Problem in Group Theory,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 44, No. 1, 1948, pp. 17-25. doi:10.1017/S030500410002394X

[2] S. C. Locke and D. Witte, “On Non-Hamiltonian Circulant Digraphs of Outdegree Three,” Journal of Graph Theory, Vol. 30, No. 4, 1999, pp. 319-331. doi:10.1002/(SICI)1097-0118(199904)30:4<319::AID-JGT6>3.0.CO;2-1

[3] D. Witte Morris, J. Morris and K. Webb, “Hamiltonian Cycles in (2,3,c)-Circulant Digraphs,” Discrete Mathematics, Vol. 309, No. 17, 2009, pp. 5484-5490. doi:10.1016/j.disc.2009.01.001

[4] ?. Miklavi and P. ?parl, “On Hamiltonicity of Circulant Digraphs of Outdegree Three,” Discrete Mathematics, Vol. 309, No. 17, 2009, pp. 5437-5443. doi:10.1016/j.disc.2008.12.004