Cayley graph associated to a semihypergroup

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.

Keywords:

Semihypergroup , Cayley graph , Fundamental relation , Category , Social network