A classification of regular -balanced Cayley maps for cyclic groups

A Cayley map M = C M ( G , X , p ) is t -balanced if p ( x ) − 1 = p t ( 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 .