J. Aust. Math. Soc.
76 (2004), 345356

Oneregular cubic graphs of order a small number times a prime or a prime square



Jin Ho Kwak
Department of Mathematics
Pohang University of Science
and Technology
Pohang
790784 Korea
jinkwak@postech.ac.kr



Abstract

A graph is oneregular if its
automorphism group acts regularly on the set of
its arcs. In this paper we show that there exists
a oneregular cubic graph of
order or where is a prime if and only if 3
is a divisor of and the graph has order greater than 25.
All of those oneregular 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
oneregular cubic graph of order or .

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