Geodesic
Hypergroups Defined on Hypergraphs and their Regular Relations
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 487 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The notion of hypergraphs, introduced around 1960, is a generalization of that of graphs and one of the initial concerns was to extend some classical results of graph theory. In this paper, we present some connections between hypergraph theory and hypergroup theory. In this regard, we construct two hypergroupoids by defining two new hyperoperations on $\mathbb{H}$, the set of all hypergraphs. We prove that our defined hypergroupoids are commutative hypergroups and we define hyperrings on $\mathbb{H}$ by using the two defined hyperoperations. Moreover, we study the fundamental group, complete parts, automorphism group and strongly regular relations of one of our hypergroups.
Classification : 20N20
Keywords: hypergraph, hypergroup, fundamental relation 
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     title = {Hypergroups {Defined} on {Hypergraphs} and their {Regular} {Relations}},
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Madeleine Al-Tahan; Bijan Davvaz. Hypergroups Defined on Hypergraphs and their Regular Relations. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 487 . http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a12/