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Graphs on which a dihedral group acts edge-transitively

✍ Scribed by Robin Sue Sanders

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
528 KB
Volume
118
Category
Article
ISSN
0012-365X

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✦ Synopsis

In the present paper we find all the graphs on which a dihedral group acts edge-transitively.

First we explicitly build the permissible permutation representations of the dihedral group. Then we use this knowledge to find all the graphs on which a dihedral group acts edge-transitively.

These graphs fall into nine types, most of which are not vertex-transitive.

The graphs which are both vertex-transitive and edge-transitive belong to a previously studied family of graphs -the well-known circulant graphs. The nonvertex-transitive graphs fall into two broad classes ~ disjoint copies of complete bipartite graphs and 'pseudo-cycles' which are related to the tensor product of a complete bipartite graph and an even cycle.

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