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Graphs and Combinatorics

, Volume 35, Issue 1, pp 321–334 | Cite as

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

  • Diogo Kendy MatsumotoEmail author
  • Atsuhiko Mizusawa
Original Paper
  • 14 Downloads

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.

Keywords

Non-confusing Simple Spanning tree Travel groupoid 

Mathematics Subject Classification

05C05 05C25 05C38 

Notes

References

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Promotion of Educational InnovationShibaura Institute of TechnologySaitamaJapan
  2. 2.Faculty of Science and EngineeringWaseda UniversityTokyoJapan

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