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An algebraic characterization of finite symmetric tournaments

Published online by Cambridge University Press:  17 April 2009

J.L. Berggren
J.L. Berggren
Affiliation:
Simon Fraser University, Burnaby, British Columbia, Canada.
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Abstract

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A tournament T is called symmetric if its automorphism group is transitive on the points and arcs of T. The main result of this paper is that if T is a finite symmetric tournament then T is isomorphic to one of the quadratic residue tournaments formed on the points of a finite field GF(pn), pn ≡ 3 (4), by the following rule: If a, b ∈ GF(pn) then there is an are directed from a to b exactly when b – a is a non-zero quadratic residue in GF(pn).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 1 , February 1972 , pp. 53 - 59
Copyright
Copyright © Australian Mathematical Society 1972

References

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