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- Levi_graph abstract "In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line. They are named for F. W. Levi, who wrote about them in 1942.The Levi graph of a system of points and lines usually has girth at least six: Any 4-cycles would correspond to two lines through the same two points. Conversely any bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure. Levi graphs of configurations are biregular, and every biregular graph with girth at least six can be viewed as the Levi graph of an abstract configuration.Levi graphs may also be defined for other types of incidence structure, such as the incidences between points and planes in Euclidean space. For every Levi graph, there is an equivalent hypergraph, and vice versa.".
- Levi_graph thumbnail Levi_graph_of_Pappus_Configuration.png?width=300.
- Levi_graph wikiPageID "1396888".
- Levi_graph wikiPageLength "5372".
- Levi_graph wikiPageOutDegree "34".
- Levi_graph wikiPageRevisionID "514913839".
- Levi_graph wikiPageWikiLink Bipartite_graph.
- Levi_graph wikiPageWikiLink Biregular_graph.
- Levi_graph wikiPageWikiLink Cage_(graph_theory).
- Levi_graph wikiPageWikiLink Category:Configurations.
- Levi_graph wikiPageWikiLink Category:Geometric_graphs.
- Levi_graph wikiPageWikiLink Category:Set_families.
- Levi_graph wikiPageWikiLink Combinatorics.
- Levi_graph wikiPageWikiLink Configuration_(geometry).
- Levi_graph wikiPageWikiLink Cremona–Richmond_configuration.
- Levi_graph wikiPageWikiLink Cycle_graph.
- Levi_graph wikiPageWikiLink Desargues_configuration.
- Levi_graph wikiPageWikiLink Desargues_graph.
- Levi_graph wikiPageWikiLink Euclidean_space.
- Levi_graph wikiPageWikiLink F._W._Levi.
- Levi_graph wikiPageWikiLink Fano_plane.
- Levi_graph wikiPageWikiLink Friedrich_Wilhelm_Levi.
- Levi_graph wikiPageWikiLink Generalized_Petersen_graph.
- Levi_graph wikiPageWikiLink Girth_(graph_theory).
- Levi_graph wikiPageWikiLink Gray_graph.
- Levi_graph wikiPageWikiLink Heawood_graph.
- Levi_graph wikiPageWikiLink Hypercube_graph.
- Levi_graph wikiPageWikiLink Hypergraph.
- Levi_graph wikiPageWikiLink Incidence_geometry.
- Levi_graph wikiPageWikiLink Incidence_structure.
- Levi_graph wikiPageWikiLink Kneser_graph.
- Levi_graph wikiPageWikiLink Ljubljana_graph.
- Levi_graph wikiPageWikiLink Möbius_configuration.
- Levi_graph wikiPageWikiLink Möbius–Kantor_configuration.
- Levi_graph wikiPageWikiLink Möbius–Kantor_graph.
- Levi_graph wikiPageWikiLink Pappus_configuration.
- Levi_graph wikiPageWikiLink Pappus_graph.
- Levi_graph wikiPageWikiLink Projective_configuration.
- Levi_graph wikiPageWikiLink Tutte_eight-cage.
- Levi_graph wikiPageWikiLink Tutte–Coxeter_graph.
- Levi_graph wikiPageWikiLink File:Levi_graph_of_Pappus_Configuration.png.
- Levi_graph wikiPageWikiLinkText "Levi graph".
- Levi_graph wikiPageWikiLinkText "incidence graph (Levi graph)".
- Levi_graph girth "≥ 6".
- Levi_graph hasPhotoCollection Levi_graph.
- Levi_graph imageCaption "The Pappus graph, a Levi graph with 18 vertices formed from the Pappus configuration. Vertices labeled with single letters correspond to points in the configuration; vertices labeled with three letters correspond to lines through three points.".
- Levi_graph name "Levi graph".
- Levi_graph title "Levi Graph".
- Levi_graph urlname "LeviGraph".
- Levi_graph wikiPageUsesTemplate Template:Infobox_graph.
- Levi_graph wikiPageUsesTemplate Template:MathWorld.
- Levi_graph wikiPageUsesTemplate Template:Reflist.
- Levi_graph subject Category:Configurations.
- Levi_graph subject Category:Geometric_graphs.
- Levi_graph subject Category:Set_families.
- Levi_graph hypernym Graph.
- Levi_graph type Software.
- Levi_graph type Combinatoric.
- Levi_graph type Concept.
- Levi_graph type Configuration.
- Levi_graph comment "In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or a projective configuration, we form a graph with one vertex per point, one vertex per line, and an edge for every incidence between a point and a line. They are named for F. W.".
- Levi_graph label "Levi graph".
- Levi_graph sameAs m.04z9sn.
- Levi_graph sameAs Граф_Леви.
- Levi_graph sameAs Q6535569.
- Levi_graph sameAs Q6535569.
- Levi_graph wasDerivedFrom Levi_graph?oldid=514913839.
- Levi_graph depiction Levi_graph_of_Pappus_Configuration.png.
- Levi_graph isPrimaryTopicOf Levi_graph.