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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 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.".
- 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 wikiPageLength "11820".
- Paley_graph wikiPageOutDegree "51".
- Paley_graph wikiPageRevisionID "691166327".
- Paley_graph wikiPageWikiLink Alfréd_Rényi.
- Paley_graph wikiPageWikiLink Block_design.
- Paley_graph wikiPageWikiLink Canadian_Mathematical_Bulletin.
- Paley_graph wikiPageWikiLink Category:Number_theory.
- Paley_graph wikiPageWikiLink Category:Parametric_families_of_graphs.
- Paley_graph wikiPageWikiLink Category:Regular_graphs.
- Paley_graph wikiPageWikiLink Category:Strongly_regular_graphs.
- Paley_graph wikiPageWikiLink Circulant_graph.
- Paley_graph wikiPageWikiLink Combinatorica.
- Paley_graph wikiPageWikiLink Conference_graph.
- Paley_graph wikiPageWikiLink Conference_matrix.
- Paley_graph wikiPageWikiLink Dense_graph.
- Paley_graph wikiPageWikiLink Directed_graph.
- Paley_graph wikiPageWikiLink Euler_characteristic.
- Paley_graph wikiPageWikiLink Expander_graph.
- Paley_graph wikiPageWikiLink Finite_field.
- Paley_graph wikiPageWikiLink Graph_theory.
- Paley_graph wikiPageWikiLink Hadamard_matrix.
- Paley_graph wikiPageWikiLink Hamiltonian_path.
- Paley_graph wikiPageWikiLink Horrocks–Mumford_bundle.
- Paley_graph wikiPageWikiLink Horst_Sachs.
- Paley_graph wikiPageWikiLink If_and_only_if.
- Paley_graph wikiPageWikiLink Journal_of_Combinatorial_Theory.
- Paley_graph wikiPageWikiLink Journal_of_Mathematical_Physics.
- Paley_graph wikiPageWikiLink Mathematics.
- Paley_graph wikiPageWikiLink Neighbourhood_(graph_theory).
- Paley_graph wikiPageWikiLink Number_theory.
- Paley_graph wikiPageWikiLink Paley_construction.
- Paley_graph wikiPageWikiLink Paul_Erdős.
- Paley_graph wikiPageWikiLink Prime_power.
- Paley_graph wikiPageWikiLink Pythagorean_prime.
- Paley_graph wikiPageWikiLink Quadratic_Gauss_sum.
- Paley_graph wikiPageWikiLink Quadratic_residue.
- Paley_graph wikiPageWikiLink Ramsey_theory.
- Paley_graph wikiPageWikiLink Raymond_Paley.
- Paley_graph wikiPageWikiLink Self-complementary_graph.
- Paley_graph wikiPageWikiLink Strongly_regular_graph.
- Paley_graph wikiPageWikiLink Subset.
- Paley_graph wikiPageWikiLink Torus.
- Paley_graph wikiPageWikiLink Tournament_(graph_theory).
- Paley_graph wikiPageWikiLink Triangulation_(topology).
- Paley_graph wikiPageWikiLink File:Paley13.svg.
- Paley_graph wikiPageWikiLinkText "Paley digraph".
- Paley_graph wikiPageWikiLinkText "Paley graph".
- Paley_graph wikiPageWikiLinkText "Paley graph#Paley digraphs".
- Paley_graph wikiPageWikiLinkText "Paley tournament".
- Paley_graph edges "q/4".
- 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 wikiPageUsesTemplate Template:Cite_conference.
- Paley_graph wikiPageUsesTemplate Template:Cite_journal.
- Paley_graph wikiPageUsesTemplate Template:Cite_web.
- Paley_graph wikiPageUsesTemplate Template:Harv.
- Paley_graph wikiPageUsesTemplate Template:Harvs.
- Paley_graph wikiPageUsesTemplate Template:Harvtxt.
- Paley_graph wikiPageUsesTemplate Template:Infobox_graph.
- Paley_graph subject Category:Number_theory.
- Paley_graph subject Category:Parametric_families_of_graphs.
- Paley_graph subject Category:Regular_graphs.
- Paley_graph subject Category:Strongly_regular_graphs.
- Paley_graph hypernym Graphs.
- Paley_graph type Field.
- Paley_graph type Redirect.
- 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 by 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 "Paley graph".
- Paley_graph sameAs Q3026495.
- Paley_graph sameAs Paley_graaf.
- Paley_graph sameAs Graphe_de_Paley.
- Paley_graph sameAs m.0f0_r1.
- Paley_graph sameAs Граф_Пейли.
- Paley_graph sameAs Paleyjev_graf.
- Paley_graph sameAs Q3026495.
- Paley_graph wasDerivedFrom Paley_graph?oldid=691166327.
- Paley_graph depiction Paley13.svg.
- Paley_graph isPrimaryTopicOf Paley_graph.