Degree hypergroupoids associated with hypergraphs | Zendy

Mehdi Farshi | Zendy; Bijan Davvaz | Zendy; S. Mirvakili | Zendy

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Degree hypergroupoids associated with hypergraphs

Author(s) -

Mehdi Farshi,

Bijan Davvaz,

S. Mirvakili

Publication year - 2014

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1401119f

Subject(s) - mathematics , degree (music) , hypergraph , cartesian product , graph , discrete mathematics , combinatorics , set (abstract data type) , graph theory , computer science , physics , acoustics , programming language

In this paper, we present some connections between graph theory and hyperstructure theory. In this regard, we construct a hypergroupoid by defining a hyperoperation on the set of degrees of vertices of a hypergraph and we call it a degree hypergroupoid. We will see that the constructed hypergroupoid is always an $H_v$-group. We will investigate some conditions on a degree hypergroupoid to have a hypergroup. Further, we study the degree hypergroupoid associated with Cartesian product of hypergraphs. Finally, the fundamental relation and complete part of a degree hypergroupoid is studied.

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