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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 wikiPageRevisionID "514913839".
- 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 subject Category:Configurations.
- Levi_graph subject Category:Geometric_graphs.
- Levi_graph subject Category:Set_families.
- Levi_graph type Abstraction100002137.
- Levi_graph type Arrangement105726596.
- Levi_graph type Cognition100023271.
- Levi_graph type Communication100033020.
- Levi_graph type Configuration105731779.
- Levi_graph type Configurations.
- Levi_graph type Design105728678.
- Levi_graph type GeometricGraphs.
- Levi_graph type Graph107000195.
- Levi_graph type PsychologicalFeature100023100.
- Levi_graph type Structure105726345.
- Levi_graph type VisualCommunication106873252.
- 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 label "Граф Леви".
- Levi_graph sameAs m.04z9sn.
- Levi_graph sameAs Q6535569.
- Levi_graph sameAs Q6535569.
- Levi_graph sameAs Levi_graph.
- Levi_graph wasDerivedFrom Levi_graph?oldid=514913839.
- Levi_graph depiction Levi_graph_of_Pappus_Configuration.png.
- Levi_graph isPrimaryTopicOf Levi_graph.