A Note on Hamiltonian Circulant Digraphs of Outdegree Three

Grant Andruchuk, Shonda Gosselin

Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, Canada.

DOI: 10.4236/ojdm.2012.24032                

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 .

Keywords

Hamilton Cycle; Circulant Digraph

Conflicts of Interest

The authors declare no conflicts of interest.

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