Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Dual_graph> ?p ?o }
- Dual_graph abstract "In the mathematical discipline of graph theory, the dual graph of a plane graph G is a graph that has a vertex for each face of G. The dual graph has an edge whenever two faces of G are separated from each other by an edge. Thus, each edge e of G has a corresponding dual edge, the edge that connects the two faces on either side of e.Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in turn generalized algebraically by the concept of a dual matroid. Variations of planar graph duality include a version of duality for directed graphs, and duality for graphs embedded onto non-planar two-dimensional surfaces.However, the notion described in this page is different from the edge-to-vertex dual (line graph) of a graph and should not be confused with it.The term "dual" is used because this property is symmetric, meaning that if H is a dual of G, then G is a dual of H (if G is connected). When discussing the dual of a graph G, the graph G itself may be referred to as the "primal graph". Many other graph properties and structures may be translated into other natural properties and structures of the dual. For instance, cycles are dual to cuts, spanning trees are dual to the complements of spanning trees, and simple graphs (without parallel edges or self-loops) are dual to 3-edge-connected graphs.Polyhedral graphs, and some other planar graphs, have unique dual graphs. However, for planar graphs more generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Testing whether one planar graph is dual to another is NP-complete.".
- Dual_graph thumbnail Duals_graphs.svg?width=300.
- Dual_graph wikiPageID "2536864".
- Dual_graph wikiPageLength "36585".
- Dual_graph wikiPageOutDegree "146".
- Dual_graph wikiPageRevisionID "681794178".
- Dual_graph wikiPageWikiLink Acyclic_orientation.
- Dual_graph wikiPageWikiLink Algorithm.
- Dual_graph wikiPageWikiLink Barnettes_conjecture.
- Dual_graph wikiPageWikiLink Biconnected_graph.
- Dual_graph wikiPageWikiLink Binary_matroid.
- Dual_graph wikiPageWikiLink Bipartite_graph.
- Dual_graph wikiPageWikiLink Bipartite_matroid.
- Dual_graph wikiPageWikiLink Bipolar_orientation.
- Dual_graph wikiPageWikiLink Bridge_(graph_theory).
- Dual_graph wikiPageWikiLink Canonical_form.
- Dual_graph wikiPageWikiLink Category:Algebraic_graph_theory.
- Dual_graph wikiPageWikiLink Category:Duality_theories.
- Dual_graph wikiPageWikiLink Category:Graph_operations.
- Dual_graph wikiPageWikiLink Category:Planar_graphs.
- Dual_graph wikiPageWikiLink Category:Topological_graph_theory.
- Dual_graph wikiPageWikiLink Circuit_rank.
- Dual_graph wikiPageWikiLink Complement_(set_theory).
- Dual_graph wikiPageWikiLink Complement_set.
- Dual_graph wikiPageWikiLink Complete_bipartite_graph.
- Dual_graph wikiPageWikiLink Complete_graph.
- Dual_graph wikiPageWikiLink Connected_space.
- Dual_graph wikiPageWikiLink Convex_hull.
- Dual_graph wikiPageWikiLink Cube_graph.
- Dual_graph wikiPageWikiLink Cubic_graph.
- Dual_graph wikiPageWikiLink Cut_(graph_theory).
- Dual_graph wikiPageWikiLink Cut_space.
- Dual_graph wikiPageWikiLink Cycle_(graph_theory).
- Dual_graph wikiPageWikiLink Cycle_basis.
- Dual_graph wikiPageWikiLink Cycle_space.
- Dual_graph wikiPageWikiLink Degree_(graph_theory).
- Dual_graph wikiPageWikiLink Delaunay_triangulation.
- Dual_graph wikiPageWikiLink Directed_acyclic_graph.
- Dual_graph wikiPageWikiLink Directed_graph.
- Dual_graph wikiPageWikiLink Drainage_basin.
- Dual_graph wikiPageWikiLink Dual_matroid.
- Dual_graph wikiPageWikiLink Dual_polyhedron.
- Dual_graph wikiPageWikiLink Dual_tessellation.
- Dual_graph wikiPageWikiLink Duality_(mathematics).
- Dual_graph wikiPageWikiLink Duncan_Sommerville.
- Dual_graph wikiPageWikiLink Equivalence_relation.
- Dual_graph wikiPageWikiLink Euler_characteristic.
- Dual_graph wikiPageWikiLink Eulerian_matroid.
- Dual_graph wikiPageWikiLink Eulerian_path.
- Dual_graph wikiPageWikiLink File:Circularmazeexample.jpg.
- Dual_graph wikiPageWikiLink Four_color_theorem.
- Dual_graph wikiPageWikiLink Fundamental_group.
- Dual_graph wikiPageWikiLink Girth_(graph_theory).
- Dual_graph wikiPageWikiLink Glossary_of_graph_theory.
- Dual_graph wikiPageWikiLink Gomory–Hu_tree.
- Dual_graph wikiPageWikiLink Graph_coloring.
- Dual_graph wikiPageWikiLink Graph_embedding.
- Dual_graph wikiPageWikiLink Graph_isomorphism.
- Dual_graph wikiPageWikiLink Graph_theory.
- Dual_graph wikiPageWikiLink Graphic_matroid.
- Dual_graph wikiPageWikiLink Halin_graph.
- Dual_graph wikiPageWikiLink Hamiltonian_cycle.
- Dual_graph wikiPageWikiLink Hamiltonian_path.
- Dual_graph wikiPageWikiLink Handshaking_lemma.
- Dual_graph wikiPageWikiLink Hassler_Whitney.
- Dual_graph wikiPageWikiLink Heawood_graph.
- Dual_graph wikiPageWikiLink Hemi-dodecahedron.
- Dual_graph wikiPageWikiLink Hemi-icosahedron.
- Dual_graph wikiPageWikiLink Hypercube_graph.
- Dual_graph wikiPageWikiLink Induced_subgraph.
- Dual_graph wikiPageWikiLink Infinite_graph.
- Dual_graph wikiPageWikiLink Jordan_curve_theorem.
- Dual_graph wikiPageWikiLink K-edge-connected_graph.
- Dual_graph wikiPageWikiLink K-vertex-connected_graph.
- Dual_graph wikiPageWikiLink Karl_Georg_Christian_von_Staudt.
- Dual_graph wikiPageWikiLink Line_graph.
- Dual_graph wikiPageWikiLink Loop_(graph_theory).
- Dual_graph wikiPageWikiLink Manifold.
- Dual_graph wikiPageWikiLink Mathematics.
- Dual_graph wikiPageWikiLink Matroid.
- Dual_graph wikiPageWikiLink Matroid_girth.
- Dual_graph wikiPageWikiLink Maze.
- Dual_graph wikiPageWikiLink Medial_graph.
- Dual_graph wikiPageWikiLink Minimum_cut.
- Dual_graph wikiPageWikiLink Minimum_spanning_tree.
- Dual_graph wikiPageWikiLink Multigraph.
- Dual_graph wikiPageWikiLink NP-complete.
- Dual_graph wikiPageWikiLink NP-completeness.
- Dual_graph wikiPageWikiLink Nowhere-zero_flow.
- Dual_graph wikiPageWikiLink Octahedron.
- Dual_graph wikiPageWikiLink Orientability.
- Dual_graph wikiPageWikiLink Outerplanar_graph.
- Dual_graph wikiPageWikiLink Petersen_graph.
- Dual_graph wikiPageWikiLink Petrie_polygon.
- Dual_graph wikiPageWikiLink Planar_graph.
- Dual_graph wikiPageWikiLink Plane_graph.
- Dual_graph wikiPageWikiLink Platonic_solid.
- Dual_graph wikiPageWikiLink Point_at_infinity.
- Dual_graph wikiPageWikiLink Polygon.
- Dual_graph wikiPageWikiLink Polyhedral_graph.