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Construction of strongly regular graphs using affine designs

Published online by Cambridge University Press:  17 April 2009

W. D. Wallis
W. D. Wallis
Affiliation:
University of Newcastle, Newcastle, New South Wales.
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Abstract

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Suppose there exist a balanced incomplete block design with λ = 1 and an affine resolvable balanced incomplete block design, the two designs having the same replication number. Combining these designs we construct two strongly regular graphs. This is applied to give a new family of design graphs ((v, k, λ)-graphs). Finally, we show that for any prime power n there are two non-isomorphic design graphs with v = n2(n+2), k = n(n+1) and λ = n.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 41 - 49
Copyright
Copyright © Australian Mathematical Society 1971

References

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