GRAPHS ON WHICH A DIHEDRAL GROUP ACTS EDGE-TRANSITIVELY

In the present paper we find all the graphs on which a dihedral group acts edge-transitively. First we explicitly build the permissible perm utation representations of the dihedral group. Then we use this knowle dge to find all the graphs on which a dihedral group acts edge-transit ively. These graphs fall into nine types, most of which are not vertex -transitive. The graphs which are both vertex-transitive and edge-tran sitive belong to a previously studied family of graphs - the well-know n circulant graphs. The nonvertex-transitive graphs fall into two broa d classes - disjoint copies of complete bipartite graphs and 'pseudo-c ycles' which are related to the tensor product of a complete bipartite graph and an even cycle.