Centered tree (original) (raw)
In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, has proved that for trees, there are only two possibilities: 1. * The tree has precisely one center (centered trees). 2. * The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent.
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| dbo:abstract | In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, has proved that for trees, there are only two possibilities: 1. * The tree has precisely one center (centered trees). 2. * The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent. A proof of this fact is given, for example, by Harary. (en) |
| dbo:thumbnail | wiki-commons:Special:FilePath/Centered_tree.gif?width=300 |
| dbo:wikiPageExternalLink | http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002153998 |
| dbo:wikiPageID | 4557120 (xsd:integer) |
| dbo:wikiPageLength | 1936 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID | 1093345758 (xsd:integer) |
| dbo:wikiPageWikiLink | dbc:Trees_(graph_theory) dbr:Tree_(graph_theory) dbr:Graph_Theory dbr:Graph_center dbr:Graph_theory dbr:Distance_(graph_theory) dbr:Vertex_(graph_theory) dbr:Mathematical dbr:Journal_für_die_reine_und_angewandte_Mathematik dbr:File:Centered_tree.gif |
| dbp:title | Bicentered Tree (en) Centered Tree (en) |
| dbp:urlname | BicenteredTree (en) CenteredTree (en) |
| dbp:wikiPageUsesTemplate | dbt:Cite_book dbt:Cite_journal dbt:Harvtxt dbt:MathWorld dbt:Mvar dbt:Short_description dbt:Use_American_English dbt:Use_mdy_dates dbt:Topology-stub |
| dcterms:subject | dbc:Trees_(graph_theory) |
| gold:hypernym | dbr:Tree |
| rdf:type | dbo:Plant |
| rdfs:comment | In the mathematical subfield of graph theory, a centered tree is a tree with only one center, and a bicentered tree is a tree with two centers. Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. However, has proved that for trees, there are only two possibilities: 1. * The tree has precisely one center (centered trees). 2. * The tree has precisely two centers (bicentered trees). In this case, the two centers are adjacent. (en) |
| rdfs:label | Centered tree (en) |
| owl:sameAs | freebase:Centered tree wikidata:Centered tree https://global.dbpedia.org/id/4gz8d |
| prov:wasDerivedFrom | wikipedia-en:Centered_tree?oldid=1093345758&ns=0 |
| foaf:depiction | wiki-commons:Special:FilePath/Centered_tree.gif |
| foaf:isPrimaryTopicOf | wikipedia-en:Centered_tree |
| is dbo:wikiPageRedirects of | dbr:Centered_Tree dbr:Bicentered_tree dbr:Bicentral_tree dbr:Central_Tree |
| is dbo:wikiPageWikiLink of | dbr:Camille_Jordan dbr:Vertex_separator dbr:Centered_Tree dbr:Bicentered_tree dbr:Bicentral_tree dbr:Central_Tree |
| is foaf:primaryTopic of | wikipedia-en:Centered_tree |
