J. Aust. Math. Soc.
81 (2006), 153164

Cubic symmetric graphs of order twice an odd primepower

YanQuan Feng
Department of Mathematics
Beijing Jiaotong University
Beijing 100044
P.R. China



Jin Ho Kwak
Combinatorial and Computational
Mathematics Center
Pohang University of Science and Technology
Pohang, 790784
Korea
jinkwak@postech.ac.kr



Abstract

An automorphism group of a graph is said to be
sregular if it acts regularly on the set of
sarcs in the graph. A graph is sregular if its full automorphism group is
sregular. For a connected cubic symmetric graph
X
of order 2p^{n} for an odd prime
p
we show that if then every Sylow
psubgroup of the full automorphism group
Aut(X)
of
X
is normal, and if then every
sregular subgroup of
Aut(X)
having a normal Sylow
psubgroup contains an
(s – 1)regular subgroup for each
. As an application, we show that every connected
cubic symmetric graph of order
2p^{n}
is a Cayley graph if p > 5 and we classify the
sregular cubic graphs of order 2p^{2}
for each
and each prime
p, as a continuation of the authors'
classification of
1regular cubic graphs of order
2p^{2}. The same classification of those of order
2p is also done.

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