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- Holt_graph abstract "In the mathematical field of graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive graph which is not also symmetric. Such graphs are not common. It is named after Peter G. Doyle and Derek F. Holt, who discovered the same graph independently in 1976 and 1981 respectively.The Holt Graph has diameter 3, radius 3 and girth 5, chromatic number 3, chromatic index 5 and is Hamiltonian with 98,472 distinct Hamiltonian cycles. It is also a 4-vertex-connected and a 4-edge-connected graph.It has an automorphism group of order 54 automorphisms. This is a smaller group than a symmetric graph with the same number of vertices and edges would have. The graph drawing on the right highlights this, in that it lacks reflectional symmetry.The characteristic polynomial of the Holt graph is".
- Holt_graph thumbnail Holt_graph.svg?width=300.
- Holt_graph wikiPageID "24240406".
- Holt_graph wikiPageRevisionID "543347532".
- Holt_graph automorphisms "54".
- Holt_graph chromaticIndex "5".
- Holt_graph chromaticNumber "3".
- Holt_graph diameter "3".
- Holt_graph edges "54".
- Holt_graph girth "5".
- Holt_graph hasPhotoCollection Holt_graph.
- Holt_graph imageCaption "In the Holt graph, all vertices are equivalent, and all edges are equivalent, but edges are not necessarily equivalent to their inverses.".
- Holt_graph name "Holt graph".
- Holt_graph namesake "Derek F. Holt".
- Holt_graph properties Cayley_graph.
- Holt_graph properties Edge-transitive_graph.
- Holt_graph properties Eulerian_path.
- Holt_graph properties Half-transitive_graph.
- Holt_graph properties Hamiltonian_path.
- Holt_graph properties Vertex-transitive_graph.
- Holt_graph radius "3".
- Holt_graph vertices "27".
- Holt_graph subject Category:Individual_graphs.
- Holt_graph subject Category:Regular_graphs.
- Holt_graph type Abstraction100002137.
- Holt_graph type Communication100033020.
- Holt_graph type Graph107000195.
- Holt_graph type IndividualGraphs.
- Holt_graph type RegularGraphs.
- Holt_graph type VisualCommunication106873252.
- Holt_graph comment "In the mathematical field of graph theory, the Holt graph or Doyle graph is the smallest half-transitive graph, that is, the smallest example of a vertex-transitive and edge-transitive graph which is not also symmetric. Such graphs are not common. It is named after Peter G. Doyle and Derek F.".
- Holt_graph label "Grafo de Holt".
- Holt_graph label "Graphe de Doyle".
- Holt_graph label "Holt graph".
- Holt_graph sameAs Graphe_de_Doyle.
- Holt_graph sameAs Grafo_de_Holt.
- Holt_graph sameAs m.07kbs93.
- Holt_graph sameAs Q3115479.
- Holt_graph sameAs Q3115479.
- Holt_graph sameAs Holt_graph.
- Holt_graph wasDerivedFrom Holt_graph?oldid=543347532.
- Holt_graph depiction Holt_graph.svg.
- Holt_graph isPrimaryTopicOf Holt_graph.
