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- 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 theta-obrazom, the covering graph, the derivative, the edge-to-vertex dual, the conjugate, and the representative graph, 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.
- Line_graph wikiPageExternalLink index.html.
- Line_graph wikiPageExternalLink e046107.
- Line_graph wikiPageID "675231".
- Line_graph wikiPageRevisionID "598582680".
- Line_graph authorlink "Hassler Whitney".
- Line_graph first "Hassler".
- Line_graph hasPhotoCollection Line_graph.
- Line_graph last "Whitney".
- Line_graph title "Line Graph".
- Line_graph urlname "LineGraph".
- Line_graph year "1932".
- Line_graph subject Category:Graph_families.
- Line_graph subject Category:Graph_operations.
- Line_graph subject Category:Intersection_classes_of_graphs.
- Line_graph type Abstraction100002137.
- Line_graph type Action114006945.
- Line_graph type Attribute100024264.
- Line_graph type Class107997703.
- Line_graph type Collection107951464.
- Line_graph type GraphOperations.
- Line_graph type Group100031264.
- Line_graph type IntersectionClassesOfGraphs.
- Line_graph type Operation114008806.
- Line_graph type State100024720.
- Line_graph comment "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.".
- Line_graph label "Graf krawędziowy".
- Line_graph label "Grafo línea".
- Line_graph label "Kantengraph".
- Line_graph label "Line graph".
- Line_graph label "Line graph".
- Line_graph label "Рёберный граф".
- Line_graph label "線圖".
- Line_graph sameAs Kantengraph.
- Line_graph sameAs Grafo_línea.
- Line_graph sameAs Line_graph.
- Line_graph sameAs 라인_그래프.
- Line_graph sameAs Graf_krawędziowy.
- Line_graph sameAs m.031zlp.
- Line_graph sameAs Q1378376.
- Line_graph sameAs Q1378376.
- Line_graph sameAs Line_graph.
- Line_graph wasDerivedFrom Line_graph?oldid=598582680.
- Line_graph isPrimaryTopicOf Line_graph.