Graduation Year


Document Type




Degree Name

Master of Arts (M.A.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Brian Curtin, Ph.D.

Committee Member

Lu Lu, Ph.D.

Committee Member

Theodore Molla, Ph.D.


Cayley Table, directed left power graph, forbidden subgraphs, Latin square, sinks


We investigate power graphs of quasigroups. The power graph of a quasigroup takes the elements of the quasigroup as its vertices, and there is an edge from one element to a second distinct element when the second is a left power of the first. We first compute the power graphs of small quasigroups (up to four elements). Next we describe quasigroups whose power graphs are directed paths, directed cycles, in-stars, out-stars, and empty. We do so by specifying partial Cayley tables, which cannot always be completed in small examples. We then consider sinks in the power graph of a quasigroup, as subquasigroups give rise to sinks. We show that certain structures cannot occur as sinks in the power graph of a quasigroup. More generally, we show that certain highly connected substructures must have edges leading out of the substructure. We briefly comment on power graphs of Bol loops.

Included in

Mathematics Commons