Finite Graphs of Valency 4 and Girth 4 Admitting Half - Transitive Group
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چکیده
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 (balanced) orientation of the edge set of a 1 2-transitive graph induced and preserved by its auto-morphism group. Among others it is proved that in a nite 1 2-transitive graph of valency 4 and girth 4 the set of 4-cycles decomposes the edge set. Moreover, in this decomposition either every 4-cycle is alternating or every 4-cycle is transitive with respect to the above orientation. In the latter case the vertex stabilizer is isomorphic to Z 2 .
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