| Title:
|
Travel groupoids (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
659-675 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, by a travel groupoid is meant an ordered pair $(V, *)$ such that $V$ is a nonempty set and $*$ is a binary operation on $V$ satisfying the following two conditions for all $u, v \in V$: \[ (u * v) * u = u; \text{ if }(u * v ) * v = u, \text{ then } u = v. \] Let $(V, *)$ be a travel groupoid. It is easy to show that if $x, y \in V$, then $x * y = y$ if and only if $y * x = x$. We say that $(V, *)$ is on a (finite or infinite) graph $G$ if $V(G) = V$ and \[ E(G) = \lbrace \lbrace u, v\rbrace \: u, v \in V \text{ and } u \ne u * v = v\rbrace . \] Clearly, every travel groupoid is on exactly one graph. In this paper, some properties of travel groupoids on graphs are studied. (English) |
| Keyword:
|
travel groupoid |
| Keyword:
|
graph |
| Keyword:
|
path |
| Keyword:
|
geodetic graph |
| MSC:
|
05C12 |
| MSC:
|
05C25 |
| MSC:
|
05C38 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1157.20336 |
| idMR:
|
MR2291765 |
| . |
| Date available:
|
2009-09-24T11:36:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128095 |
| . |
| Reference:
|
[1] G. Chartrand, L. Lesniak: Graphs & Digraphs. Third edition.Chapman & Hall, London, 1996. MR 1408678 |
| Reference:
|
[2] L. Nebeský: An algebraic characterization of geodetic graphs.Czechoslovak Math. J. 48(123) (1998), 701–710. MR 1658245, 10.1023/A:1022435605919 |
| Reference:
|
[3] L. Nebeský: A tree as a finite nonempty set with a binary operation.Math. Bohem. 125 (2000), 455–458. MR 1802293 |
| Reference:
|
[4] L. Nebeský: New proof of a characterization of geodetic graphs.Czechoslovak Math. J. 52(127) (2002), 33–39. MR 1885455, 10.1023/A:1021715219620 |
| Reference:
|
[5] L. Nebeský: On signpost systems and connected graphs.Czechoslovak Math. J. 55(130) (2005), 283–293. MR 2137138, 10.1007/s10587-005-0022-0 |
| . |
