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Relation Algebras andt-vertex Condition Graphs

✍ Scribed by J. WojdyŁo

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 120 KB
Volume: 19
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1998.0244

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✦ Synopsis

The scheme associated with a graph is an association scheme iff the graph is strongly regular. Consider the problem of extending such an association scheme to a superscheme. The obstacles can be expressed in terms of t-vertex conditions. If a graph does not satisfy the t-vertex condition, a presuperscheme associated with it cannot be erected beyond the (t -3)rd level. We give an example of an association scheme which is not extendible to a superscheme: it cannot be extended beyond the bottom level of a presuperscheme.

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