Orderly Algorithm to enumerate central groupoids and their graphs
Rings and Algebras
2007-05-23 v1 Combinatorics
Abstract
A graph has the unique path property UPP_n if there is a unique path of length n between any ordered pair of nodes. This paper reiterates Royle and MacKay's technique for constructing orderly algorithms. We wish to use this technique to enumerate all UPP_2 graphs of small orders 9 and 16. We attempt to use the direct graph formalism and find that the algorithm is inefficient. We introduce a generalised problem and derive algebraic and combinatoric structures with appropriate structure. We are able to then design an orderly algorithm to determine all UPP_2 graphs of order 9, which runs fast enough. We hope to be able to determine the UPP_2 graphs of order 16 in the near future.
Cite
@article{arxiv.math/0407070,
title = {Orderly Algorithm to enumerate central groupoids and their graphs},
author = {Tim Boykett},
journal= {arXiv preprint arXiv:math/0407070},
year = {2007}
}
Comments
21 pages, 6 figures