Let X, G be a primitive commutative association scheme. If g g G is nonsym-ลฝ . metric of valency 4, then the graph X, g is uniquely determined up to isomorphism. In particular, the cardinality of X is the cube of an odd prime. แฎ 1999 ## X Let r : X = X be given. We set < r\* [ x, y y, x g r , ร 4
Fusion Relation in Products of Association Schemes
โ Scribed by Sung Y. Song
- Publisher
- Springer Japan
- Year
- 2002
- Tongue
- English
- Weight
- 140 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0911-0119
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๐ SIMILAR VOLUMES
Let (X, [R i ] 0 i d ) be a primitive commutative association scheme. If there is a non-symmetric relation R i with valency 3, then the cardinality of X is equal to either p or p 2 where p is an odd prime. Moreover, if |X | = p then (X, [R i ] 0 i d ) is isomorphic to a cyclotomic scheme.
In this paper we will define the product of two association schemes and using the fact that the strong product of two graphs from two (possibly different) association schemes is in the product of the association schemes, we give a new proof of Schrijver's result on the Shannon capacity of graphs in