T-partition systems and travel groupoids on a graph
Combinatorics
2015-12-02 v1 Discrete Mathematics
Abstract
The notion of travel groupoids was introduced by L. Nebesk\'y in 2006 in connection with a study on geodetic graphs. A travel groupoid is a pair of a set and a binary operation on satisfying two axioms. For a travel groupoid, we can associate a graph. We say that a graph has a travel groupoid if the graph associated with the travel groupoid is equal to . Nebesk\'y gave a characterization for finite graphs to have a travel groupoid. In this paper, we introduce the notion of T-partition systems on a graph and give a characterization of travel groupoids on a graph in terms of T-partition systems.
Cite
@article{arxiv.1512.00363,
title = {T-partition systems and travel groupoids on a graph},
author = {Jung Rae Cho and Jeongmi Park and Yoshio Sano},
journal= {arXiv preprint arXiv:1512.00363},
year = {2015}
}
Comments
10 pages