Orderly Algorithm to enumerate central groupoids and their graphs
| dc.creator | Boykett, Tim | |
| dc.date | 2004-07-05 | |
| dc.date.accessioned | 2026-07-07T05:09:58Z | |
| dc.date.available | 2026-07-07T05:09:58Z | |
| dc.description | 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. | |
| dc.description | 21 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/math/0407070 | |
| dc.identifier | http://arxiv.org/abs/math/0407070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71780 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Combinatorics | |
| dc.subject | 05C30, 05C38, 05C50, 05C12 | |
| dc.title | Orderly Algorithm to enumerate central groupoids and their graphs | |
| dc.type | text |