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- Distance-transitive_graph abstract "In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.A distance transitive graph is vertex transitive and symmetric as well as distance regular. A distance-transitive graph is interesting partly because it has a large automorphism group. Some interesting finite groups are the automorphism groups of distance-transitive graphs, especially of those whose diameter is 2.Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and D. H. Smith, who showed that there are only 12 finite trivalent distance-transitive graphs. These are:Independently in 1969 a Russian group led by Georgy Adelson-Velsky showed that there exist graphs that are distance-regular but not distance-transitive. The only graph of this type with degree three is the 126-vertex Tutte 12-cage. The smallest distance-regular graph that is not distance-transitive is the Shrikhande graph. Complete lists of distance-transitive graphs are known for some degrees larger than three, but the classification of distance-transitive graphs with arbitrarily large vertex degree remains open.The simplest asymptotic family of examples of distance-transitive graphs is the Hypercube graphs. Other families are the folded cube graphs and the square rook's graphs. All three of these families have arbitrarily high degree.".
- Distance-transitive_graph thumbnail BiggsSmith.svg?width=300.
- Distance-transitive_graph wikiPageID "7768222".
- Distance-transitive_graph wikiPageRevisionID "544581844".
- Distance-transitive_graph hasPhotoCollection Distance-transitive_graph.
- Distance-transitive_graph title "Distance-Transitive Graph".
- Distance-transitive_graph urlname "Distance-TransitiveGraph".
- Distance-transitive_graph subject Category:Algebraic_graph_theory.
- Distance-transitive_graph subject Category:Graph_families.
- Distance-transitive_graph subject Category:Regular_graphs.
- Distance-transitive_graph type Abstraction100002137.
- Distance-transitive_graph type Family108078020.
- Distance-transitive_graph type GraphFamilies.
- Distance-transitive_graph type Group100031264.
- Distance-transitive_graph type Organization108008335.
- Distance-transitive_graph type SocialGroup107950920.
- Distance-transitive_graph type Unit108189659.
- Distance-transitive_graph type YagoLegalActor.
- Distance-transitive_graph type YagoLegalActorGeo.
- Distance-transitive_graph type YagoPermanentlyLocatedEntity.
- Distance-transitive_graph comment "In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y.A distance transitive graph is vertex transitive and symmetric as well as distance regular. A distance-transitive graph is interesting partly because it has a large automorphism group.".
- Distance-transitive_graph label "Distance-transitive graph".
- Distance-transitive_graph label "Grafo distância-transitivo".
- Distance-transitive_graph label "Дистанционно-транзитивный граф".
- Distance-transitive_graph label "距離推移グラフ".
- Distance-transitive_graph sameAs 距離推移グラフ.
- Distance-transitive_graph sameAs Grafo_distância-transitivo.
- Distance-transitive_graph sameAs m.026cdlx.
- Distance-transitive_graph sameAs Q4391306.
- Distance-transitive_graph sameAs Q4391306.
- Distance-transitive_graph sameAs Distance-transitive_graph.
- Distance-transitive_graph wasDerivedFrom Distance-transitive_graph?oldid=544581844.
- Distance-transitive_graph depiction BiggsSmith.svg.
- Distance-transitive_graph isPrimaryTopicOf Distance-transitive_graph.
