A Note on Hamiltonian Circulant Digraphs of Outdegree Three

DOI: 10.4236/ojdm.2012.24032   PDF   HTML     3,148 Downloads   4,947 Views  

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 .

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[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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