Some implications on amorphic association schemes

E.R. van Dam, M. Muzychuk

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Abstract

We give an overview of results on amorphic association schemes.
We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.
Original languageEnglish
Pages (from-to)111-127
JournalJournal of Combinatorial Theory, Series A, Structures designs and application combinatorics
Volume117
Publication statusPublished - 2010

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Association Scheme
Association reactions
Complete Graph
Decomposition
Decompose
Strongly Regular Graph
Cyclotomic
Union

Cite this

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title = "Some implications on amorphic association schemes",
abstract = "We give an overview of results on amorphic association schemes.We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.",
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Some implications on amorphic association schemes. / van Dam, E.R.; Muzychuk, M.

In: Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics, Vol. 117, 2010, p. 111-127.

Research output: Contribution to journalArticleScientificpeer-review

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N2 - We give an overview of results on amorphic association schemes.We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.

AB - We give an overview of results on amorphic association schemes.We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.

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JO - Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics

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