Multiples of left loops and vertex-transitive graphs (Q2496102)

The author proves that every finite vertex-transitive graph \(G\) is isomorphic to a groupoid graph \(\text{GG}(Q,S)\) where \(Q\) is a left loop with a right unit and \(S\subseteq Q\) is a quasi-associative Cayley set. Moreover, \(\text{GG}(Q, S)\) is a vertex-transitive graph if \(Q\) is a left loop with a right unit and \(S\subseteq Q\) is a quasi-associative Cayley set.