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T-neighbor Systems and Travel Groupoids on a Graph

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Abstract

The notion of travel groupoids was introduced by 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. Nebeský gave a characterization for finite graphs to have a travel groupoid. In this paper, we introduce the notion of T-neighbor systems on a graph and give a characterization of travel groupoids on a graph in terms of T-neighbor systems.

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References

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Acknowledgements

Yoshio Sano’s work was supported by JSPS KAKENHI Grant Numbers 25887007, JP15K20885, JP16H03118.

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Authors and Affiliations

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

    Jung Rae Cho

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

    Jeongmi Park

  3. Division of Information Engineering, Faculty of Engineering, Information and Systems, University of Tsukuba, 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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Correspondence to Yoshio Sano.

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Cho, J.R., Park, J. & Sano, Y. T-neighbor Systems and Travel Groupoids on a Graph. Graphs and Combinatorics 33, 1521–1529 (2017). https://doi.org/10.1007/s00373-017-1850-z

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  • DOI: https://doi.org/10.1007/s00373-017-1850-z

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