J. Austral. Math. Soc.
73 (2002), 155-170
|
Finite graphs of valency 4 and girth 4 admitting half-transitive group actions
|
Dragan Marusic
IMFM, Oddelek za matematiko
Univerza v Ljubljani
Jadranska 19
1000 Ljubljana
Slovenija
dragan.marusic@uni-lj.si
|
|
|
Roman Nedela
Katedra Matematiky
Univerzita Mateja Bela
975 49 Banská Bystrica
Slovensko
nedela@bb.sanet.sk
|
|
|
Abstract
|
Finite graphs of valency 4 and girth 4 admitting
1/2-transitive group actions, that is, vertex-
and edge- but not arc-transitive group actions,
are investigated. A graph is said to be 1/2-transitive
if its automorphism group acts
1/2-transitively. There is a natural orientation
of the edge set of a 1/2-transitive graph induced
and preserved by its automorphism group. It is
proved that in a finite 1/2-transitive graph of
valency 4 and girth 4 the set of 4-cycles
decomposes the edge set in such a way that either
every 4-cycle is alternating or every 4-cycle is
directed relative to this orientation. In the
latter case vertex stabilizers are isomorphic
to  .
|
Download the article in PDF format (size 148 Kb)
|
|
|
|