BabelNet

bn:01883958n

Noun Concept

Categories: Graph operations, Topological graph theory, Algebraic graph theory, Duality theories, Planar graphs

dual graph Algebraic dual graph planar dual self-dual graph weak dual

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 for each pair of faces in G that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Wikipedia

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Graph theory construction exchanging vertices and faces Wikidata

A graph derived from some plane graph in such a way that the derived graph has a vertex corresponding to each face of the given graph, an edge corresponding to each edge of the given graph that is shared by a pair of distinct faces, and a self-loop for each edge of the given graph that is a border of the same face on both of its sides. Wiktionary

The edges of a dual graph are perpendicular, in some sense, to the edges of its original graph. The dual graph also has as many vertices and faces as its original graph has faces and vertices, respectively. Therefore the dual graph has the same Euler characteristic as its original graph. Wiktionary

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Algebraic dual graph, planar dual, self-dual graph, weak dual, Weak dual graph, Whitney planarity criterion