Distance-transitive dihedrants

Abstract

The main result of this article is a classification of distance-transitive Cayley graphs on dihedral groups. We show that a Cayley graph X on a dihedral group is distance-transitive if and only if X is isomorphic to one of the following graphs: the complete graph K 2n ; a complete multipartite graph K t×m with t anticliques of size m, where t m is even; the complete bipartite graph without 1-factor K n,n ? nK 2; the cycle C 2n ; the incidence or the non-incidence graph of the projective geometry PG d-1(d,q), d ? 2; the incidence or the non-incidence graph of a symmetric design on 11 vertices.