J. Aust. Math. Soc.
81 (2006), 153-164|
Cubic symmetric graphs of order twice an odd prime-power
Department of Mathematics
Beijing Jiaotong University
Jin Ho Kwak|
Combinatorial and Computational
Pohang University of Science and Technology
| An automorphism group of a graph is said to be
s-regular if it acts regularly on the set of
s-arcs in the graph. A graph is s-regular if its full automorphism group is
s-regular. For a connected cubic symmetric graph
of order 2pn for an odd prime
we show that if then every Sylow
p-subgroup of the full automorphism group
is normal, and if then every
s-regular subgroup of
having a normal Sylow
p-subgroup contains an
(s – 1)-regular subgroup for each
. As an application, we show that every connected
cubic symmetric graph of order
is a Cayley graph if p > 5 and we classify the
s-regular cubic graphs of order 2p2
and each prime
p, as a continuation of the authors'
1-regular cubic graphs of order
2p2. The same classification of those of order
2p is also done.
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