Cayley graph associated to a semihypergroup
نویسندگان
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
doi
10.22034/as.2020.1792چکیده
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.
