جستجوی مقالات مرتبط با کلیدواژه « Semihypergroup » در نشریات گروه « ریاضی »

The study of hyperstructures derived from particular mathematical objects is very important and interesting. Graph theory has been established as a fundamental and important tool for solving practical problems in other branches of mathematics. This paper can be considered as one of the connections between hyperstructures and graph theory. In this way, by using the dominating set notion of a graph, we define a hyperoperation on verticals of it and study its properties and then we construct a hypergroup based on this hyperoperation. This hypergroup is presented for some classes of graphs.

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.

In this paper, we introduce and study the concepts of prime left, semiprime left and irreducible left hyperideals in ternary semihyper- groups and investigate some basic properties of them. We introduce the concepts of hyper lter and hypersemilattice congruence of ternary semi- hypergroups. We give some characterizations of hyper lters in ternary semihypergroups. Some relationships between hyper lters, prime hyper- ideals and hypersemilattice congruences in ternary semihypergroups are considered. We also introduce the notion of hyperideals extensions in ternary semihypergroups and some properties of them are investigated.