Path hypergroupoids: Commutativity and graph connectivity

The path hyperoperation, a generalization of Corsini’s hyperoperation deriving from graph theory, was recently introduced and applied for assembly line designing. In this paper we study the commutativity property for the corresponding class of hypergroupoids and investigate their connection with Graph Theory. Moreover, we prove that such a (partial) hypergroupoid is commutative if and only if it can be obtained as a disjoint union of non-partial hypergroupoids.