East Asian mathematical journal

  • 제35권1호
  • /
  • Pages.17-22
  • /
  • 2019
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  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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CHARACTERIZATION OF TRAVEL GROUPOIDS BY PARTITION SYSTEMS ON GRAPHS

  • Cho, Jung Rae (Department of Mathematics, Pusan National University) ;
  • Park, Jeongmi (Faculty of Engineering, Information and Systems, University of Tsukuba)
  • 투고 : 2018.09.06
  • 심사 : 2018.10.20
  • 발행 : 2019.01.31
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초록

A travel groupoid is a pair (V, ${\ast}$) of a set V and a binary operation ${\ast}$ on V satisfying two axioms. For a travel groupoid, we can associate a graph in a certain manner. For a given graph G, we say that a travel groupoid (V, ${\ast}$) is on G if the graph associated with (V, ${\ast}$) is equal to G. There are some results on the classification of travel groupoids which are on a given graph [1, 2, 3, 9]. In this article, we introduce the notion of vertex-indexed partition systems on a graph, and classify the travel groupoids on the graph by the those vertex-indexed partition systems.

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참고문헌

  1. J. R. Cho, J. Park, and Y. Sano: Travel groupoids on infinite graphs, Czechoslovak Mathematical Journal 64 (2014) 763-766. https://doi.org/10.1007/s10587-014-0130-9
  2. J. R. Cho, J. Park, and Y. Sano: The non-confusing travel groupoids on a finite connected graph, Lecture Notes in Computer Science 8845 (2014) 14-17.
  3. J. R. Cho, J. Park, and Y. Sano: T-neighbor systems and travel groupoids on a graph, Graphs and Combinatorics 33 (2017) 1521-1529. https://doi.org/10.1007/s00373-017-1850-z
  4. L. Nebesky: An algebraic characterization of geodetic graphs, Czechoslovak Mathematical Journal 48(123) (1998) 701-710. https://doi.org/10.1023/A:1022435605919
  5. L. Nebesky: A tree as a finite nonempty set with a binary operation, Mathematica Bohemica 125 (2000) 455-458. https://doi.org/10.21136/MB.2000.126275
  6. L. Nebesky: New proof of a characterization of geodetic graphs, Czechoslovak Mathematical Journal 52(127) (2002) 33-39. https://doi.org/10.1023/A:1021715219620
  7. L. Nebesky: On signpost systems and connected graphs, Czechoslovak Mathematical Journal 55(130) (2005) 283-293. https://doi.org/10.1007/s10587-005-0022-0
  8. L. Nebesky: Travel groupoids, Czechoslovak Mathematical Journal 56(131) (2006) 659-675. https://doi.org/10.1007/s10587-006-0046-0
  9. D. K. Matsumoto and A. Mizusawa: A construction on smooth travel groupoids on finite graphs, Graphs and Combinatorics 32 (2016) 1117-1124. https://doi.org/10.1007/s00373-015-1630-6