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. For a travel groupoid, we can associate a graph. We say that a graph \(G\) has a travel groupoid if the graph associated with the travel groupoid is equal to \(G\). A travel groupoid is said to be non-confusing if it has no confusing pairs. Nebeský showed that every finite connected graph has at least one non-confusing travel groupoid.
In this note, we study non-confusing travel groupoids on a given finite connected graph and we give a one-to-one correspondence between the set of all non-confusing travel groupoids on a finite connected graph and a combinatorial structure in terms of the given graph.
Jung Rae Cho—This research was supported for two years by Pusan National University Research Grant.
Yoshio Sano—This work was supported by JSPS KAKENHI grant number 25887007.
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Cho, J.R., Park, J., Sano, Y. (2014). The Non-confusing Travel Groupoids on a Finite Connected Graph. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_2
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DOI: https://doi.org/10.1007/978-3-319-13287-7_2
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