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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 447-455 |
| Number of pages | 9 |
| Journal | Miskolc Mathematical Notes |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2023 |
Keywords
- Cayley color graph
- groupoid
- line graph
- partial automorphism
- semidirect product
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Numerical Analysis
- Discrete Mathematics and Combinatorics
- Control and Optimization