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An algebraic characterization of finite symmetric tournaments
Published online by Cambridge University Press: 17 April 2009
Abstract
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).
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- Copyright © Australian Mathematical Society 1972
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