A classification of regular t-balanced Cayley maps for cyclic groups

A Cayley map M=CM(G,X,p) is t-balanced if p(x)−1=pt(x−1) for all x∈X. Recently, Conder et al. classified the regular anti-balanced Cayley maps for abelian groups and Kwak et al. classified the regular t-balanced Cayley maps for dihedral groups [8] and dicyclic groups [9]. Oh [11] classified the regular t-balanced Cayley maps for semi-dihedral groups. In this paper, we classify the regular t-balanced Cayley maps for cyclic groups for any t.