Cayley hypergraphs and Cayley hypermaps

In this paper, we introduce a Cayley hypergraph which is a generalization of a Cayley graph, and a Cayley hypermap which is a generalization of a Cayley map. We investigate some properties of Cayley hypergraphs and Cayley hypermaps, describe the automorphism group of a Cayley hypermap and determine when a Cayley hypermap is regular.