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

摘要

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