# Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes

@article{Tanaka2011NonexistenceOE,
title={Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes},
author={Hajime Tanaka and Rie Tanaka},
journal={Eur. J. Comb.},
year={2011},
volume={32},
pages={155-161}
}
• Published 20 May 2010
• Mathematics
• Eur. J. Comb.
9 Citations
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• Mathematics, Computer Science
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It is proved that the deletion of the neighborhood of any vertex leaves behind at most one non-singleton component, and the only connected relations in symmetric association schemes which admit a disconnecting set of size two are those which are ordinary polygons.
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• 2021
In this paper we show that if θ is a T -design of an association scheme (Ω , R ), and the Krein parameters q hi,j vanish for some h 6∈ T and all i, j 6∈ T ( i, j, h 6 = 0), then θ consists of

## References

SHOWING 1-9 OF 9 REFERENCES
Commutative association schemes
• Mathematics
Eur. J. Comb.
• 2009
Imprimitive Q-polynomial Association Schemes
AbstractIt is well known that imprimitive P-polynomial association schemes $$\mathcal{X} = (X,\{ R_i \} _{0 \leqslant i \leqslant d} )$$ with  are either bipartite or antipodal, i.e.,
Distance-Regular Graphs
• Mathematics
• 2007