"Orderly Algorithm to Enumerate Central Groupoids and Their Graphs"
, in Acta Mathematica Sinica, Serie English, Vol. 23, Nummer 2, Springer, Seite(n) 249-264, 2-2007, ISSN: 1439-8516
Orderly Algorithm to Enumerate Central Groupoids and Their Graphs
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Abstract A graph has the unique path property UPPn 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 UPP2 graphs of small orders 32 and 42 . 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. Then we are able to design an orderly algorithm to determine all UPP2 graphs of order 3^2 , which runs fast enough. We hope to be able to determine the UPP2 graphs of order 4^2 in the