Graphs and Combinatorics

, Volume 35, Issue 1, pp 321–334

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

• Diogo Kendy Matsumoto
• Atsuhiko Mizusawa
Original Paper

## 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

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