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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 onto the Klein bottle so that it forms a map requiring six colors, showing that six colors are sometimes necessary in this case.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 wikiPageRevisionID "550049951".
- Franklin_graph automorphisms "48".
- Franklin_graph chromaticIndex "3".
- Franklin_graph chromaticNumber "2".
- Franklin_graph diameter "3".
- Franklin_graph edges "18".
- 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_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 subject Category:Individual_graphs.
- Franklin_graph subject Category:Regular_graphs.
- Franklin_graph type Abstraction100002137.
- Franklin_graph type Communication100033020.
- Franklin_graph type Graph107000195.
- Franklin_graph type IndividualGraphs.
- Franklin_graph type RegularGraphs.
- Franklin_graph type VisualCommunication106873252.
- 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 label "Graphe de Franklin".
- Franklin_graph sameAs Graphe_de_Franklin.
- Franklin_graph sameAs m.06zqb7t.
- Franklin_graph sameAs Q3115484.
- Franklin_graph sameAs Q3115484.
- Franklin_graph sameAs Franklin_graph.
- Franklin_graph wasDerivedFrom Franklin_graph?oldid=550049951.
- Franklin_graph depiction Franklin_graph_hamiltonian.svg.
- Franklin_graph isPrimaryTopicOf Franklin_graph.
