  Let $\Gamma$ be a simple undirected graph on a finite vertex set and let $A$
be its adjacency matrix. Then $\Gamma$ is {\it singular} if $A$ is singular.
The problem of characterising singular graphs is easy to state but very
difficult to resolve in any generality. In this paper we investigate the
singularity of graphs for which the dihedral group acts transitively on
vertices as a group of automorphisms.
