Skip to main content
SpringerLink
Log in

Characterizations of the Simple Non-Confusing Travel Groupoids on a Finite Graph

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

A travel groupoid is an algebraic system related to graphs, which was defined by Nebeský in 2006. In this article, we characterize simple non-confusing travel groupoids on a finite graph in two ways. One is given by using spanning trees of the graph and the other by its subgroupoids. Furthermore, we introduce a way to construct a simple non-confusing travel groupoid on a given finite graph by using the spanning trees, and we count numbers of simple non-confusing travel groupoids on cycle graphs and cactus graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Cho, J.R., Park, J., Sano, Y.: The non-confusing travel groupoids on a finite connected graph. Lect. Notes Comput. Sci. 8845, 14–17 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cho, J.R., Park, J., Sano, Y.: Travel groupoids on infinite graphs. Czechoslov. Math. J. 64, 763–766 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cho, J.R., Park, J., Sano, Y.: \(T\)-neighbor systems and travel groupoids on a graph. Graphs Comb. 33(6), 1521–1529 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Matsumoto, D.K., Mizusawa, A.: A construction of smooth travel groupoids on finite graphs. Graphs Comb. 32(3), 1117–1124 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Nebeský, L.: A tree as a finite nonempty set with a binary operation. Math. Bohem. 125, 455–458 (2000)

    MathSciNet  MATH  Google Scholar 

  7. Nebeský, L.: New proofs of a characterization of geodetic graphs. Czechoslov. Math. J. 52(127), 33–39 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nebeský, L.: Travel groupoids. Czechoslov. Math. J. 56(131), 659–675 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Promotion of Educational Innovation, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama, Saitama, 337-8570, Japan

    Diogo Kendy Matsumoto

  2. Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Atsuhiko Mizusawa

Authors
  1. Diogo Kendy Matsumoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atsuhiko Mizusawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Diogo Kendy Matsumoto.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matsumoto, D.K., Mizusawa, A. Characterizations of the Simple Non-Confusing Travel Groupoids on a Finite Graph. Graphs and Combinatorics 35, 321–334 (2019). https://doi.org/10.1007/s00373-018-1995-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-018-1995-4

Keywords

Mathematics Subject Classification

Search

Navigation