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- Pappus_graph abstract "In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is named after Pappus of Alexandria, an ancient Greek mathematician who is believed to have discovered the "hexagon theorem" describing the Pappus configuration. All the cubic distance-regular graphs are known; the Pappus graph is one of the 13 such graphs.The Pappus graph has rectilinear crossing number 5, and is the smallest cubic graph with that crossing number (sequence A110507 in OEIS). It has girth 6, diameter 4, radius 4, chromatic number 2, chromatic index 3 and is both 3-vertex-connected and 3-edge-connected.The Pappus graph has a chromatic polynomial equal to: .The name "Pappus graph" has also been used to refer to a related nine-vertex graph, with a vertex for each point of the Pappus configuration and an edge for every pair of points on the same line; this nine-vertex graph is 6-regular, and is the complement graph of the union of three disjoint triangle graphs. The first Pappus graph can be embedded in the torus to form a regular map with nine hexagonal faces; the second, to form a regular map with 18 triangular faces.".
- Pappus_graph thumbnail Pappus_graph_LS.svg?width=300.
- Pappus_graph wikiPageID "7250518".
- Pappus_graph wikiPageRevisionID "588878370".
- Pappus_graph automorphisms "216".
- Pappus_graph chromaticIndex "3".
- Pappus_graph chromaticNumber "2".
- Pappus_graph diameter "4".
- Pappus_graph edges "27".
- Pappus_graph girth "6".
- Pappus_graph hasPhotoCollection Pappus_graph.
- Pappus_graph imageCaption "The Pappus graph.".
- Pappus_graph name "Pappus graph".
- Pappus_graph namesake Pappus_of_Alexandria.
- Pappus_graph properties Bipartite_graph.
- Pappus_graph properties Cubic_graph.
- Pappus_graph properties Distance-regular_graph.
- Pappus_graph properties Distance-transitive_graph.
- Pappus_graph properties Hamiltonian_path.
- Pappus_graph properties Symmetric_graph.
- Pappus_graph radius "4".
- Pappus_graph vertices "18".
- Pappus_graph subject Category:Individual_graphs.
- Pappus_graph subject Category:Regular_graphs.
- Pappus_graph type Abstraction100002137.
- Pappus_graph type Communication100033020.
- Pappus_graph type Graph107000195.
- Pappus_graph type IndividualGraphs.
- Pappus_graph type RegularGraphs.
- Pappus_graph type VisualCommunication106873252.
- Pappus_graph comment "In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges, formed as the Levi graph of the Pappus configuration. It is named after Pappus of Alexandria, an ancient Greek mathematician who is believed to have discovered the "hexagon theorem" describing the Pappus configuration.".
- Pappus_graph label "Grafo de Pappus".
- Pappus_graph label "Graphe de Pappus".
- Pappus_graph label "Pappus graph".
- Pappus_graph label "Граф Паппа".
- Pappus_graph sameAs Graphe_de_Pappus.
- Pappus_graph sameAs Grafo_de_Pappus.
- Pappus_graph sameAs m.025x7qk.
- Pappus_graph sameAs Q3115526.
- Pappus_graph sameAs Q3115526.
- Pappus_graph sameAs Pappus_graph.
- Pappus_graph wasDerivedFrom Pappus_graph?oldid=588878370.
- Pappus_graph depiction Pappus_graph_LS.svg.
- Pappus_graph isPrimaryTopicOf Pappus_graph.
