Multiary Quasigroups
Just as a group expansion of a complete graph Kn encodes the group (see Dowling geometry), its combinatorial analog expanding a simple cycle of length n + 1 encodes an n-ary (multiary) quasigroup. It is possible to prove theorems about multiary quasigroups by means of biased graphs (Zaslavsky, t.a.)
Read more about this topic: Biased Graph