A classification of regular -balanced Cayley maps on dihedral groups

In their study of regular t -balanced Cayley maps on a group, Conder et al. [M. Conder, R. Jajcay, T. Tucker, Regular t -balanced Cayley maps, J. Combin. Theory Ser. B (in press)] recently classified the regular anti-balanced Cayley maps on an abelian group. In this paper, we classify the regular t -balanced Cayley maps on a dihedral group for any t .