Geodesic
Travel groupoids on infinite graphs
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 763-766 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 
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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

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