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- Paley_graph 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 in 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.".
- Paley_graph thumbnail Paley13.svg?width=300.
- Paley_graph wikiPageExternalLink v12i1n15.html.
- Paley_graph wikiPageExternalLink P0506_PaleyGenus.html.
- Paley_graph wikiPageExternalLink Paley.html.
- Paley_graph wikiPageID "5719307".
- Paley_graph wikiPageRevisionID "581739540".
- Paley_graph edges "q/4".
- Paley_graph hasPhotoCollection Paley_graph.
- Paley_graph imageCaption "The Paley graph of order 13".
- Paley_graph name "Paley graph".
- Paley_graph namesake Raymond_Paley.
- Paley_graph notation "QR".
- Paley_graph properties Conference_graph.
- Paley_graph properties Self-complementary_graph.
- Paley_graph properties Strongly_regular_graph.
- Paley_graph vertices "q prime power".
- Paley_graph vertices "q ≡ 1 mod 4,".
- Paley_graph subject Category:Number_theory.
- Paley_graph subject Category:Parametric_families_of_graphs.
- Paley_graph subject Category:Regular_graphs.
- Paley_graph type Abstraction100002137.
- Paley_graph type Communication100033020.
- Paley_graph type Graph107000195.
- Paley_graph type RegularGraphs.
- Paley_graph type VisualCommunication106873252.
- Paley_graph 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 in a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices.".
- Paley_graph label "Graphe de Paley".
- Paley_graph label "Paley graph".
- Paley_graph label "Граф Пейли".
- Paley_graph sameAs Graphe_de_Paley.
- Paley_graph sameAs m.0f0_r1.
- Paley_graph sameAs Q3026495.
- Paley_graph sameAs Q3026495.
- Paley_graph sameAs Paley_graph.
- Paley_graph wasDerivedFrom Paley_graph?oldid=581739540.
- Paley_graph depiction Paley13.svg.
- Paley_graph isPrimaryTopicOf Paley_graph.