Directed Graphs representing isomorphism classes of C-Hypergroupoids

Abstract

We investigate the relation of directed graphs and hyperstructures by virtue of the graph hyperoperation. A new class of graphs arises in this way representing isomorphism classes of C-hypergroupoids and we present the 17 such graphs that correspond to the 73 C-hypergroupoids associated with binary relations on three element sets. As it is shown they constitute an upper semilattice with respect to graph inclusion.

Keywords

• Hyperoperations, Hypergroupoids, Directed Graphs.