A classification of regular Cayley maps with trivial Cayley-core for dihedral groups

Let M=CM(G,X,p) be a regular Cayley map for the finite group G, and let Aut+(M) be the orientation-preserving automorphism group of M. Then G can be regarded as a subgroup of Aut+(M) in the sense that G acts on itself by left multiplication. The core of G in Aut+(M) is called the Cayley-core of M. In this paper, the regular Cayley maps with trivial Cayley-core for dihedral groups are classified. This work is a partial result for our long term goal to classify all regular Cayley maps for dihedral groups.