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Japanese Conference on Discrete and Computational Geometry and Graphs

JCDCGG 2013: Discrete and Computational Geometry and Graphs pp 14–17Cite as

The Non-confusing Travel Groupoids on a Finite Connected Graph

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

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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References

  1. Nebeský, L.: An algebraic characterization of geodetic graphs. Czech. Math. J. 48(123), 701–710 (1998)

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Author information

Authors and Affiliations

  1. Department of Mathematics, Pusan National University, Busan, 609-735, Korea

    Jung Rae Cho & Jeongmi Park

  2. Division of Information Engineering, Faculty of Engineering, Information and Systems, University of Tsukuba, Ibaraki, 305-8573, Japan

    Yoshio Sano

Authors
  1. Jung Rae Cho
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  2. Jeongmi Park
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  3. Yoshio Sano
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Corresponding author

Correspondence to Jeongmi Park .

Editor information

Editors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications, Tokyo, Japan

    Hiro Ito

  3. Tokai University, Tokyo, Japan

    Toshinori Sakai

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© 2014 Springer International Publishing Switzerland

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Cite this paper

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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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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