J. Austral. Math. Soc.
73 (2002), 155170

Finite graphs of valency 4 and girth 4 admitting halftransitive group actions

Dragan Marusic
IMFM, Oddelek za matematiko
Univerza v Ljubljani
Jadranska 19
1000 Ljubljana
Slovenija
dragan.marusic@unilj.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
1/2transitive group actions, that is, vertex
and edge but not arctransitive group actions,
are investigated. A graph is said to be 1/2transitive
if its automorphism group acts
1/2transitively. There is a natural orientation
of the edge set of a 1/2transitive graph induced
and preserved by its automorphism group. It is
proved that in a finite 1/2transitive graph of
valency 4 and girth 4 the set of 4cycles
decomposes the edge set in such a way that either
every 4cycle is alternating or every 4cycle is
directed relative to this orientation. In the
latter case vertex stabilizers are isomorphic
to .

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