Automorphism Groups of Cayley Maps

Cayley maps are embeddings of Cayley graphs in orientable surfaces, with the same local orientation at every vertex. In this paper, conditions will be given under which a Cayley map is regular or reflexible, together with algorithms for checking these conditions. We shall give the description of the automorphism group of an arbitrary Cayley map and focus on the special case of k-balanced Cayley maps.