Travel groupoids on infinite graphs
Jung Rae Cho; Jeongmi Park; Yoshio Sano
Czechoslovak Mathematical Journal (2014)
- Volume: 64, Issue: 3, page 763-766
- ISSN: 0011-4642
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topCho, Jung Rae, Park, Jeongmi, and Sano, Yoshio. "Travel groupoids on infinite graphs." Czechoslovak Mathematical Journal 64.3 (2014): 763-766. <http://eudml.org/doc/262204>.
@article{Cho2014,
abstract = {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.},
author = {Cho, Jung Rae, Park, Jeongmi, Sano, Yoshio},
journal = {Czechoslovak Mathematical Journal},
keywords = {travel groupoid; geodetic graph; infinite graph; travel groupoid; geodetic graph; infinite graph},
language = {eng},
number = {3},
pages = {763-766},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Travel groupoids on infinite graphs},
url = {http://eudml.org/doc/262204},
volume = {64},
year = {2014},
}
TY - JOUR
AU - Cho, Jung Rae
AU - Park, Jeongmi
AU - Sano, Yoshio
TI - Travel groupoids on infinite graphs
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 763
EP - 766
AB - 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.
LA - eng
KW - travel groupoid; geodetic graph; infinite graph; travel groupoid; geodetic graph; infinite graph
UR - http://eudml.org/doc/262204
ER -
References
top- Nebeský, L., 10.1023/A:1022435605919, Czech. Math. J. 48 (1998), 701-710. (1998) Zbl0949.05022MR1658245DOI10.1023/A:1022435605919
- Nebeský, L., A tree as a finite nonempty set with a binary operation, Math. Bohem. 125 (2000), 455-458. (2000) Zbl0963.05032MR1802293
- Nebeský, L., 10.1023/A:1021715219620, Czech. Math. J. 52 (2002), 33-39. (2002) Zbl0995.05124MR1885455DOI10.1023/A:1021715219620
- Nebeský, L., 10.1007/s10587-005-0022-0, Czech. Math. J. 55 (2005), 283-293. (2005) Zbl1081.05054MR2137138DOI10.1007/s10587-005-0022-0
- Nebeský, L., 10.1007/s10587-006-0046-0, Czech. Math. J. 56 (2006), 659-675. (2006) Zbl1157.20336MR2291765DOI10.1007/s10587-006-0046-0
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