Geodesic
Travel groupoids on infinite graphs
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 763-766

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

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.
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.
DOI : 10.1007/s10587-014-0130-9
Classification : 05C12, 05C63, 20N02
Keywords: travel groupoid; geodetic graph; infinite graph 
Cho, Jung Rae; Park, Jeongmi; Sano, Yoshio. Travel groupoids on infinite graphs. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 763-766. doi: 10.1007/s10587-014-0130-9
@article{10_1007_s10587_014_0130_9,
     author = {Cho, Jung Rae and Park, Jeongmi and Sano, Yoshio},
     title = {Travel groupoids on infinite graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {763--766},
     year = {2014},
     volume = {64},
     number = {3},
     doi = {10.1007/s10587-014-0130-9},
     mrnumber = {3298558},
     zbl = {06391523},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0130-9/}
}
TY  - JOUR
AU  - Cho, Jung Rae
AU  - Park, Jeongmi
AU  - Sano, Yoshio
TI  - Travel groupoids on infinite graphs
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 763
EP  - 766
VL  - 64
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0130-9/
DO  - 10.1007/s10587-014-0130-9
LA  - en
ID  - 10_1007_s10587_014_0130_9
ER  - 
%0 Journal Article
%A Cho, Jung Rae
%A Park, Jeongmi
%A Sano, Yoshio
%T Travel groupoids on infinite graphs
%J Czechoslovak Mathematical Journal
%D 2014
%P 763-766
%V 64
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0130-9/
%R 10.1007/s10587-014-0130-9
%G en
%F 10_1007_s10587_014_0130_9

[1] Nebeský, L.: An algebraic characterization of geodetic graphs. Czech. Math. J. 48 (1998), 701-710. | DOI | MR | Zbl

[2] Nebeský, L.: A tree as a finite nonempty set with a binary operation. Math. Bohem. 125 (2000), 455-458. | MR | Zbl

[3] Nebeský, L.: New proof of a characterization of geodetic graphs. Czech. Math. J. 52 (2002), 33-39. | DOI | MR | Zbl

[4] Nebeský, L.: On signpost systems and connected graphs. Czech. Math. J. 55 (2005), 283-293. | DOI | MR | Zbl

[5] Nebeský, L.: Travel groupoids. Czech. Math. J. 56 (2006), 659-675. | DOI | MR | Zbl

Cité par Sources :