Locally primitive Cayley graphs of dihedral groups

A graph ΓΓ is called locally-primitive   if the vertex stabilizer (AutΓ)α is primitive on the neighbor set of αα for each vertex αα. In this paper, we classify locally-primitive Cayley graphs of dihedral groups, while 2-arc-transitive Cayley graphs of dihedral groups have been classified by a series of papers in the literature.