Cayley graph associated to a semihypergroup

Abstract

The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as Hamiltonian cycles in this graph. Also, by some of examples we will illustrate the properties and behavior of these Cayley graphs, in particulars we show that the properties of a Cayley graph associated to a semihypergroup is completely different with respect to the Cayley graph associated to a semigroup(group). Also, we briefly discuss on category of Cayley graphs associated to semihypergroups and construct a functor from this category to the category of digraphs. Finally, we give an application the Cayley graph of a hypergroupoid to a social network.