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.