Characterization and construction of Cayley graphs admitting regular Cayley maps (Q1815316)

This paper addresses the question of which Cayley graphs can be the underlying graph of a regular Cayley map. A Cayley map is an embedding of a Cayley graph into an orientable surface such that the cyclic ordering of the edges around each vertex is the same. The map is regular if its group of map-automorphisms is as large as possible (making it arc-transitive). In a previous paper the author characterized the regular Cayley maps as those Cayley maps having a ``rotary mapping.'' In this paper he uses that result to characterize the underlying Cayley graphs, first in terms of a graph-automorphism property and then in terms of the presentation (relations) for the associated finite group.