Nonnormal edge-transitive cubic Cayley graphs of dihedral groups (Q643164)

Summary: A Cayley graph of a finite group \(G\) is called normal edge transitive if its automorphism group has a subgroup which both normalizes \(G\) and acts transitively on edges. In this paper we determine all cubic, connected, and undirected edge-transitive Cayley graphs of dihedral groups, which are not normal edge transitive. This is a partial answer to the question of \textit{C. E. Praeger} [Bull. Aust. Math. Soc. 60, No. 2, 207--220 (1999; Zbl 0939.05047)].