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- Tietze's_graph abstract "In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges, formed by applying a Y-Δ transform to the Petersen graph and thereby replacing one of its vertices by a triangle.Tietze's graph has chromatic number 3, chromatic index 4, girth 3 and diameter 3. The independence number is 5. Its automorphism group has order 12, and is isomorphic to the dihedral group D6, the group of symmetries of an hexagon, including both rotations and reflections. This group has two orbits of size 3 and one of size 6 on vertices, and thus this graph is not vertex-transitive.Like the Petersen graph it is maximally nonhamiltonian: it has no Hamiltonian cycle, but any two non-adjacent vertices can be connected by a Hamiltonian path. It and the Petersen graph are the only 2-vertex-connected cubic non-Hamiltonian graphs with 12 or fewer vertices.Tietze's graph matches part of the definition of a snark: it is a cubic bridgeless graph that is not 3-edge-colorable. However, some authors restrict snarks to graphs without 3-cycles and 4-cycles, and under this more restrictive definition Tietze's graph is not a snark. Tietze's graph is isomorphic to the graph J3, part of an infinite family of flower snarks introduced by R. Isaacs in 1975.".
- Tietze's_graph thumbnail Tietze's_graph.svg?width=300.
- Tietze's_graph wikiPageID "20058152".
- Tietze's_graph wikiPageRevisionID "545488749".
- Tietze's_graph automorphisms "12".
- Tietze's_graph chromaticIndex "4".
- Tietze's_graph chromaticNumber "3".
- Tietze's_graph diameter "3".
- Tietze's_graph edges "18".
- Tietze's_graph girth "3".
- Tietze's_graph hasPhotoCollection Tietze's_graph.
- Tietze's_graph imageCaption "The Tietze graph".
- Tietze's_graph name "Tietze's graph".
- Tietze's_graph properties Cubic_graph.
- Tietze's_graph properties Snark_(graph_theory).
- Tietze's_graph vertices "12".
- Tietze's_graph subject Category:Individual_graphs.
- Tietze's_graph subject Category:Regular_graphs.
- Tietze's_graph type Abstraction100002137.
- Tietze's_graph type Communication100033020.
- Tietze's_graph type Graph107000195.
- Tietze's_graph type IndividualGraphs.
- Tietze's_graph type RegularGraphs.
- Tietze's_graph type VisualCommunication106873252.
- Tietze's_graph comment "In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges, formed by applying a Y-Δ transform to the Petersen graph and thereby replacing one of its vertices by a triangle.Tietze's graph has chromatic number 3, chromatic index 4, girth 3 and diameter 3. The independence number is 5.".
- Tietze's_graph label "Graphe de Tietze".
- Tietze's_graph label "Tietze's graph".
- Tietze's_graph sameAs Graphe_de_Tietze.
- Tietze's_graph sameAs m.04yh0tj.
- Tietze's_graph sameAs Q3115539.
- Tietze's_graph sameAs Q3115539.
- Tietze's_graph sameAs Tietze's_graph.
- Tietze's_graph wasDerivedFrom Tietze's_graph?oldid=545488749.
- Tietze's_graph depiction Tietze's_graph.svg.
- Tietze's_graph isPrimaryTopicOf Tietze's_graph.