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- Q3026495 subject Q10185811.
- Q3026495 subject Q7217289.
- Q3026495 subject Q8647012.
- Q3026495 abstract "In mathematics, and specifically graph theory, Paley graphs, named after Raymond Paley, are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic tools to be applied to the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally.Paley graphs are closely related to the Paley construction for constructing Hadamard matrices from quadratic residues (Paley 1933).They were introduced as graphs independently by Sachs (1962) and Erdős & Rényi (1963). Sachs was interested in them for their self-complementarity properties, while Erdős and Rényi studied their symmetries.Paley digraphs are directed analogs of Paley graphs that yield antisymmetric conference matrices. They were introduced by Graham & Spencer (1971) (independently of Sachs, Erdős, and Rényi) as a way of constructing tournaments with a property previously known to be held only by random tournaments: in a Paley digraph, every small subset of vertices is dominated by some other vertex.".
- Q3026495 thumbnail Paley13.svg?width=300.
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- Q3026495 comment "In mathematics, and specifically graph theory, Paley graphs, named after Raymond Paley, are dense undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices.".
- Q3026495 label "Paley graph".
- Q3026495 depiction Paley13.svg.
