MMN-1651

# Cayley line graphs of transitive groupoids

*Nándor Sieben*;

## Abstract

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

DOI: 10.18514/MMN.2023.1651