| Title:
|
Travel groupoids on infinite graphs (English) |
| Author:
|
Cho, Jung Rae |
| Author:
|
Park, Jeongmi |
| Author:
|
Sano, Yoshio |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
763-766 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of travel groupoids was introduced by L. Nebeský in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set $V$ and a binary operation $*$ on $V$ satisfying two axioms. We can associate a graph with a travel groupoid. We say that a graph $G$ has a travel groupoid if the graph associated with the travel groupoid is equal to $G$. Nebeský gave a characterization of finite graphs having a travel groupoid. In this paper, we study travel groupoids on infinite graphs. We answer a question posed by Nebeský, and we also give a characterization of infinite graphs having a travel groupoid. (English) |
| Keyword:
|
travel groupoid |
| Keyword:
|
geodetic graph |
| Keyword:
|
infinite graph |
| MSC:
|
05C12 |
| MSC:
|
05C63 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 06391523 |
| idMR:
|
MR3298558 |
| DOI:
|
10.1007/s10587-014-0130-9 |
| . |
| Date available:
|
2014-12-19T16:09:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144056 |
| . |
| Reference:
|
[1] Nebeský, L.: An algebraic characterization of geodetic graphs.Czech. Math. J. 48 (1998), 701-710. Zbl 0949.05022, MR 1658245, 10.1023/A:1022435605919 |
| Reference:
|
[2] Nebeský, L.: A tree as a finite nonempty set with a binary operation.Math. Bohem. 125 (2000), 455-458. Zbl 0963.05032, MR 1802293 |
| Reference:
|
[3] Nebeský, L.: New proof of a characterization of geodetic graphs.Czech. Math. J. 52 (2002), 33-39. Zbl 0995.05124, MR 1885455, 10.1023/A:1021715219620 |
| Reference:
|
[4] Nebeský, L.: On signpost systems and connected graphs.Czech. Math. J. 55 (2005), 283-293. Zbl 1081.05054, MR 2137138, 10.1007/s10587-005-0022-0 |
| Reference:
|
[5] Nebeský, L.: Travel groupoids.Czech. Math. J. 56 (2006), 659-675. Zbl 1157.20336, MR 2291765, 10.1007/s10587-006-0046-0 |
| . |
