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- Distance-regular_graph abstract "In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i = d(v, w).In particular, this holds when k = 1: in a distance-regular graph, for any two vertices v and w at distance i the number of vertices adjacent to w and at distance j from v is the same. It turns out that, conversely, this implies the above definition of distance-regularity. Therefore, an equivalent definition is that a distance-regular graph is a graph for which there exist integers bi,ci,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly ci neighbors of y in Gi-1(x) and bi neighbors of y in Gi+1(x), where Gi(x) is the set of vertices y of G with d(x,y)=i (Brouwer et al., p. 434). The array of integers characterizing a distance-regular graph is known as its intersection array.Every distance-transitive graph is distance regular. Indeed, distance-regular graphs were introduced as a combinatorial generalization of distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group.A distance-regular graph with diameter 2 is strongly regular, and conversely (unless the graph is disconnected).".
- Distance-regular_graph wikiPageID "7768943".
- Distance-regular_graph wikiPageRevisionID "592196198".
- Distance-regular_graph hasPhotoCollection Distance-regular_graph.
- Distance-regular_graph subject Category:Algebraic_graph_theory.
- Distance-regular_graph subject Category:Graph_families.
- Distance-regular_graph subject Category:Regular_graphs.
- Distance-regular_graph type Abstraction100002137.
- Distance-regular_graph type Family108078020.
- Distance-regular_graph type GraphFamilies.
- Distance-regular_graph type Group100031264.
- Distance-regular_graph type Organization108008335.
- Distance-regular_graph type SocialGroup107950920.
- Distance-regular_graph type Unit108189659.
- Distance-regular_graph type YagoLegalActor.
- Distance-regular_graph type YagoLegalActorGeo.
- Distance-regular_graph type YagoPermanentlyLocatedEntity.
- Distance-regular_graph comment "In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i = d(v, w).In particular, this holds when k = 1: in a distance-regular graph, for any two vertices v and w at distance i the number of vertices adjacent to w and at distance j from v is the same. It turns out that, conversely, this implies the above definition of distance-regularity.".
- Distance-regular_graph label "Distance-regular graph".
- Distance-regular_graph label "Grafo distância-regular".
- Distance-regular_graph label "Graphe distance-régulier".
- Distance-regular_graph label "Дистанционно-регулярный граф".
- Distance-regular_graph sameAs Graphe_distance-régulier.
- Distance-regular_graph sameAs Grafo_distância-regular.
- Distance-regular_graph sameAs m.026cfpz.
- Distance-regular_graph sameAs Q3115556.
- Distance-regular_graph sameAs Q3115556.
- Distance-regular_graph sameAs Distance-regular_graph.
- Distance-regular_graph wasDerivedFrom Distance-regular_graph?oldid=592196198.
- Distance-regular_graph isPrimaryTopicOf Distance-regular_graph.