Cayley graph associated to a semihypergroup

Document Type : Research Paper


1 Department of Mathematics, Payamenoor University, P.O. Box 19395-4697, Tehran, Iran

2 Department of mathematics, University of Tehran, Tehran, Iran.

3 Department of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran



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 the
properties 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.


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