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 OJDM  Vol.2 No.4 , October 2012
A Note on Hamiltonian Circulant Digraphs of Outdegree Three
Grant Andruchuk, Shonda Gosselin
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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
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.
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

 
 
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