Some Normal Edge-transitive Cayley Graphs on Dihedral Groups

Let ?? be a group and ?? a subset of ?? such that 1 ?? ? ?? and ?? = ?? ?1 . Let ?? = ??????(??, ??) be a Cayley graph on ?? relative to. Then ?? is said to be normal edge-transitive, if ?? (??) acts transitively on edges. In this paper we determine all normal edge-transitive Cayley graphs on a dihedral Group ?? ?????? (??) of valency ?? . In addition we classify normal edge-transitive Cayley graphs ?? = ??????(?? , ??) of valency four, for a prime ?? and give some normal edge-transitive Cayley graphs ?? = ??????(?? , ??) of valency four that ?? is not a prime . 2?? 2?? 2??