Abstract
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 language | English |
|---|---|
| Pages (from-to) | 111-127 |
| Journal | Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics |
| Volume | 117 |
| Publication status | Published - 2010 |
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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 journal › Article › Scientific › peer-review
TY - JOUR
T1 - Some implications on amorphic association schemes
AU - van Dam, E.R.
AU - Muzychuk, M.
N1 - Appeared earlier as CentER Discussion Paper 2008-56
PY - 2010
Y1 - 2010
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.
M3 - Article
VL - 117
SP - 111
EP - 127
JO - Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics
JF - Journal of Combinatorial Theory, Series A, Structures designs and application combinatorics
SN - 0097-3165
ER -