Regular maps from Cayley graphs, part 1: Balanced Cayley maps

Skoviera, M. and J. ‘&Iii, Regular maps from Cayley graphs, Part i: Balanced Cayley maps, Discrete Mathematics IO9 (1992) 265-276. A Cayley map is a Cayley graph 2-cell embedded in some orientable surface so that the local rotations at every vertex are identical. Two types of Cayley maps are introduced: the balanced and antibalanced Cayley maps. In Part 1, conditions are given uuder which a balanced Cayley map is regular or reflexible, and automorphism groups of such maps are determined. In addition, a characterization of regular balanced Cayley maps is presented.