A classification of regular tt-balanced Cayley maps on dicyclic groups

A Cayley map CM(G,S,p) is a 2-cell embedding of a Cayley graph Cay(G,S) into an orientable surface such that all vertex-rotations correspond to the cyclic permutation pp of the generating set SS. It is called regular if its automorphism group acts regularly on the dart set. A regular Cayley map M=CM(G,S,p) is called tt-balanced if p(x)−1=pt(x−1)p(x)−1=pt(x−1) for every x∈Sx∈S. In this paper, we classify the regular tt-balanced Cayley maps on dicyclic groups for all tt. As a result, all such maps are 1-balanced.