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- Cage_(graph_theory) abstract "In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at leastvertices, and any cage with even girth g must have at leastvertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries-Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).".
- Cage_(graph_theory) thumbnail Tutte_eight_cage.svg?width=300.
- Cage_(graph_theory) wikiPageExternalLink allcages.html.
- Cage_(graph_theory) wikiPageExternalLink index.html.
- Cage_(graph_theory) wikiPageExternalLink pdf.
- Cage_(graph_theory) wikiPageExternalLink 1966-06.pdf.
- Cage_(graph_theory) wikiPageExternalLink cages.html.
- Cage_(graph_theory) wikiPageID "7735022".
- Cage_(graph_theory) wikiPageRevisionID "600827190".
- Cage_(graph_theory) hasPhotoCollection Cage_(graph_theory).
- Cage_(graph_theory) title "Cage Graph".
- Cage_(graph_theory) urlname "CageGraph".
- Cage_(graph_theory) subject Category:Graph_families.
- Cage_(graph_theory) subject Category:Regular_graphs.
- Cage_(graph_theory) type Abstraction100002137.
- Cage_(graph_theory) type Family108078020.
- Cage_(graph_theory) type GraphFamilies.
- Cage_(graph_theory) type Group100031264.
- Cage_(graph_theory) type Organization108008335.
- Cage_(graph_theory) type SocialGroup107950920.
- Cage_(graph_theory) type Unit108189659.
- Cage_(graph_theory) type YagoLegalActor.
- Cage_(graph_theory) type YagoLegalActorGeo.
- Cage_(graph_theory) type YagoPermanentlyLocatedEntity.
- Cage_(graph_theory) comment "In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3.".
- Cage_(graph_theory) label "Cage (graph theory)".
- Cage_(graph_theory) label "Cage (graphe)".
- Cage_(graph_theory) label "Клетка (теория графов)".
- Cage_(graph_theory) sameAs Cage_(graphe).
- Cage_(graph_theory) sameAs m.026bb9x.
- Cage_(graph_theory) sameAs Q841007.
- Cage_(graph_theory) sameAs Q841007.
- Cage_(graph_theory) sameAs Cage_(graph_theory).
- Cage_(graph_theory) wasDerivedFrom Cage_(graph_theory)?oldid=600827190.
- Cage_(graph_theory) depiction Tutte_eight_cage.svg.
- Cage_(graph_theory) isPrimaryTopicOf Cage_(graph_theory).
