Cayley line graphs of transitive groupoidsNándor Sieben;
A groupoid is a small category with inverses. Adding appropriate colors to the edges of the line graph of a transitive groupoid creates a Cayley line graph of the groupoid. The groupoid of partial automorphisms of the Cayley line graph is isomorphic to a semidirect product of the original groupoid. Using the trivial coloring to build the Cayley line graph makes the semidirect product trivial, hence the groupoid of partial automorphisms of this Cayley line graph is isomorphic to the original groupoid.
Vol. 24 (2023), No. 1, pp. 447-455