Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Line_graph> ?p ?o }
- Line_graph abstract "In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this. Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the ϑ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph.Hassler Whitney (1932) proved that with one exceptional case the structure of a connected graph G can be recovered completely from its line graph. Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs can be characterized by nine forbidden subgraphs, and can be recognized in linear time.Various generalizations of line graphs have also been studied, including the line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs.".
- Line_graph wikiPageExternalLink gc_249.html.
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- Line_graph wikiPageWikiLink Adjacency_matrix.
- Line_graph wikiPageWikiLink Adjacent_(graph_theory).
- Line_graph wikiPageWikiLink Articulation_point.
- Line_graph wikiPageWikiLink Biconnected_component.
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- Line_graph wikiPageWikiLink Block_graph.
- Line_graph wikiPageWikiLink Bridge_(graph_theory).
- Line_graph wikiPageWikiLink Brute-force_search.
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- Line_graph wikiPageWikiLink Category:Graph_families.
- Line_graph wikiPageWikiLink Category:Graph_operations.
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- Line_graph wikiPageWikiLink Chang_graphs.
- Line_graph wikiPageWikiLink Circolo_Matematico_di_Palermo.
- Line_graph wikiPageWikiLink Claw-free_graph.
- Line_graph wikiPageWikiLink Claw_(graph_theory).
- Line_graph wikiPageWikiLink Clique_(graph_theory).
- Line_graph wikiPageWikiLink Complement_(graph_theory).
- Line_graph wikiPageWikiLink Complement_graph.
- Line_graph wikiPageWikiLink Complete_bipartite_graph.
- Line_graph wikiPageWikiLink Complete_graph.
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- Line_graph wikiPageWikiLink Connectivity_(graph_theory).
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- Line_graph wikiPageWikiLink Cycle_(graph_theory).
- Line_graph wikiPageWikiLink Cycle_graph.
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- Line_graph wikiPageWikiLink Degree_distribution.
- Line_graph wikiPageWikiLink Diamond_graph.
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- Line_graph wikiPageWikiLink Hamiltonian_path.
- Line_graph wikiPageWikiLink Handshaking_lemma.
- Line_graph wikiPageWikiLink Hypergraph.
- Line_graph wikiPageWikiLink Independent_set_(graph_theory).
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- Line_graph wikiPageWikiLink Rendiconti_del_Circolo_Matematico_di_Palermo.