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- Franklin_graph abstract "In the mathematical field of graph theory, the Franklin graph a 3-regular graph with 12 vertices and 18 edges.The Franklin graph is named after Philip Franklin, who disproved the Heawood conjecture on the number of colors needed when a two-dimensional surface is partitioned into cells by a graph embedding. The Heawood conjecture implied that the maximum chromatic number of a map on the Klein bottle should be seven, but Franklin proved that in this case six colors always suffice. The Franklin graph can be embedded in the Klein bottle so that it forms a map requiring six colors, showing that six colors are sometimes necessary in this case. This embedding is the Petrie dual of its embedding in the projective plane shown below.It is Hamiltonian and has chromatic number 2, chromatic index 3, radius 3, diameter 3 and girth 4. It is also a 3-vertex-connected and 3-edge-connected perfect graph.".
- Franklin_graph thumbnail Franklin_graph_hamiltonian.svg?width=300.
- Franklin_graph wikiPageID "23717056".
- Franklin_graph wikiPageLength "3115".
- Franklin_graph wikiPageOutDegree "38".
- Franklin_graph wikiPageRevisionID "671968864".
- Franklin_graph wikiPageWikiLink Bipartite_graph.
- Franklin_graph wikiPageWikiLink Category:Individual_graphs.
- Franklin_graph wikiPageWikiLink Category:Regular_graphs.
- Franklin_graph wikiPageWikiLink Characteristic_polynomial.
- Franklin_graph wikiPageWikiLink Chromatic_index.
- Franklin_graph wikiPageWikiLink Chromatic_number.
- Franklin_graph wikiPageWikiLink Cubic_graph.
- Franklin_graph wikiPageWikiLink Cyclic_group.
- Franklin_graph wikiPageWikiLink Direct_product_of_groups.
- Franklin_graph wikiPageWikiLink Edge_coloring.
- Franklin_graph wikiPageWikiLink Girth_(graph_theory).
- Franklin_graph wikiPageWikiLink Graph_automorphism.
- Franklin_graph wikiPageWikiLink Graph_coloring.
- Franklin_graph wikiPageWikiLink Graph_embedding.
- Franklin_graph wikiPageWikiLink Graph_theory.
- Franklin_graph wikiPageWikiLink Group_direct_product.
- Franklin_graph wikiPageWikiLink Hamiltonian_graph.
- Franklin_graph wikiPageWikiLink Hamiltonian_path.
- Franklin_graph wikiPageWikiLink Heawood_conjecture.
- Franklin_graph wikiPageWikiLink Hemi-octahedron.
- Franklin_graph wikiPageWikiLink K-edge-connected_graph.
- Franklin_graph wikiPageWikiLink K-vertex-connected_graph.
- Franklin_graph wikiPageWikiLink Klein_bottle.
- Franklin_graph wikiPageWikiLink Mathematics.
- Franklin_graph wikiPageWikiLink Perfect_graph.
- Franklin_graph wikiPageWikiLink Petrie_polygon.
- Franklin_graph wikiPageWikiLink Philip_Franklin.
- Franklin_graph wikiPageWikiLink Projective_plane.
- Franklin_graph wikiPageWikiLink Regular_graph.
- Franklin_graph wikiPageWikiLink Symmetric_group.
- Franklin_graph wikiPageWikiLink Triangle-free_graph.
- Franklin_graph wikiPageWikiLink Truncation_(geometry).
- Franklin_graph wikiPageWikiLink Vertex-transitive_graph.
- Franklin_graph wikiPageWikiLink File:Franklin_graph_hamiltonian.svg.
- Franklin_graph wikiPageWikiLinkText "Franklin graph".
- Franklin_graph automorphisms "48".
- Franklin_graph chromaticIndex "3".
- Franklin_graph chromaticNumber "2".
- Franklin_graph diameter "3".
- Franklin_graph edges "18".
- Franklin_graph genus "1".
- Franklin_graph girth "4".
- Franklin_graph hasPhotoCollection Franklin_graph.
- Franklin_graph imageCaption "The Franklin Graph".
- Franklin_graph name "Franklin Graph".
- Franklin_graph namesake Philip_Franklin.
- Franklin_graph properties Bipartite_graph.
- Franklin_graph properties Cubic_graph.
- Franklin_graph properties Hamiltonian_graph.
- Franklin_graph properties Hamiltonian_path.
- Franklin_graph properties Perfect_graph.
- Franklin_graph properties Triangle-free_graph.
- Franklin_graph properties Vertex-transitive_graph.
- Franklin_graph radius "3".
- Franklin_graph vertices "12".
- Franklin_graph wikiPageUsesTemplate Template:Commons_category.
- Franklin_graph wikiPageUsesTemplate Template:Infobox_graph.
- Franklin_graph wikiPageUsesTemplate Template:Reflist.
- Franklin_graph subject Category:Individual_graphs.
- Franklin_graph subject Category:Regular_graphs.
- Franklin_graph type Graph.
- Franklin_graph comment "In the mathematical field of graph theory, the Franklin graph a 3-regular graph with 12 vertices and 18 edges.The Franklin graph is named after Philip Franklin, who disproved the Heawood conjecture on the number of colors needed when a two-dimensional surface is partitioned into cells by a graph embedding. The Heawood conjecture implied that the maximum chromatic number of a map on the Klein bottle should be seven, but Franklin proved that in this case six colors always suffice.".
- Franklin_graph label "Franklin graph".
- Franklin_graph sameAs Graphe_de_Franklin.
- Franklin_graph sameAs m.06zqb7t.
- Franklin_graph sameAs Q3115484.
- Franklin_graph sameAs Q3115484.
- Franklin_graph wasDerivedFrom Franklin_graph?oldid=671968864.
- Franklin_graph depiction Franklin_graph_hamiltonian.svg.
- Franklin_graph isPrimaryTopicOf Franklin_graph.
