2089

Obtaining non-commutative hypergroups(Hv-groups) and polygroups from the concept of neighborhood and diameter of graphs and directed graphs

دكتري تخصصي

رياضي محض گرايش جبر

مركز تحصيلات تكميلي دانشگاه پيام نور

1402

1402/06/27

دكتر سعيد ميروكيلي، دكتر پيمان غياثوند

دكتر محمد حميدي

Graph, Hypergraph, Non-commutative Hypergroup, Non-commutative Hv- group, Polygroup

The topic of our study in this thesis is investigating the connection between graph theory (hypergraph theory) and hyperstructure theory that many researchers have worked on. In most studies, a hypergroupoid associated with a hypergraph is constructed by defining a hyperoperation on the set of vertices of that hypergraph. Many hypergraphs associated with graphs (hypergraphs) are built and presented using this method such that most of them were commutative or weak commutative. Hence, we try to introduce a graph that gives us a non-weak commutative Hv-group by defining a suitable hyperoperation on the set of its vertices. Generalization of this hyperoperation makes more hyperstructures associated with graphs. Also, we know that polygroup has a similar structure to the group. On the other side, obtaining groups associated with graphs is rarely studied. This is why we try to use the method that Comer presented to build polygroups associate with distance-regular graphs. Building hyperstructures associated with directed graphs is another topic in this thesis.

1403/08/09

ابراهيمي

76642