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1 results

  • One-regular cubic graphs of order a small number times a prime or a prime square

  • Part of
  • Yan-Quan Feng, Jin Ho Kwak
  • Journal:
    Journal of the Australian Mathematical Society / Volume 76 / Issue 3 / June 2004
    Published online by Cambridge University Press:
    09 April 2009, pp. 345-356
    Print publication:
    June 2004
    • Article
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  • A graph is one-regular if its automorphism group acts regularly on the set of its arcs. In this paper we show that there exists a one-regular cubic graph of order 2p or 2p2 where p is a prime if and only if 3 is a divisor of p – 1 and the graph has order greater than 25. All of those one-regular cubic graphs are Cayley graphs on dihedral groups and there is only one such graph for each fixed order. Surprisingly, it can be shown that there is no one-regular cubic graph of order 4p or 4p2.