mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

dual. The dual graph depends on how the primal graph is embedded: different planar embeddings of a single graph may lead to different dual graphs. Matroid...

form a graph embedded on this surface, and the vertices and edges of the (abstract) dual polyhedron form the dual graph of the original graph. An abstract...

from the similarly-named notions of a dual polyhedron, and of the dual graph of a surface-embedded graph. Dual graphs have also been used to define and study...

graphs, named after Hassler Whitney. It states that a graph G is planar if and only if its graphic matroid is also cographic (that is, it is the dual...

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...

In topological graph theory, the Petrie dual of an embedded graph (on a 2-manifold with all faces disks) is another embedded graph that has the Petrie...

as: edge contraction, line graph, dual graph, complement graph, graph rewriting; binary operations, which create a new graph from two initial ones, such...

In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that...

hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two...

In planar graphs, dijoins and feedback arc sets are dual concepts. The dual graph of a directed graph, embedded in the plane, is a graph with a vertex...

useful graph that is often associated with a triangulation of a polygon P is the dual graph. Given a triangulation TP of P, one defines the graph G(TP)...

In the mathematical field of graph theory, the Dyck graph is a 3-regular graph with 32 vertices and 48 edges, named after Walther von Dyck. It is Hamiltonian...

In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar...

Nauru graph is a toroidal graph: it consists of 12 hexagonal faces together with the 24 vertices and 36 edges of the Nauru graph. The dual graph of this...

every wheel graph is a Halin graph. They are self-dual: the planar dual of any wheel graph is an isomorphic graph. Every maximal planar graph, other than...

of graph; dual graph; medial graph; quotient graph; Y-Δ transform; Mycielskian. Binary operations create a new graph from two initial graphs G1 = (V1,...

the orientable surface of genus 3, in which they form dual graphs. This is a 3-regular (cubic) graph with 56 vertices and 84 edges, named after Felix Klein...

other. The dual of a graph can be found entirely by a graphical method. The dual of a graph is another graph. For a given tree in a graph, the complementary...

In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability...

just a vertex coloring of its line graph, and a face coloring of a plane graph is just a vertex coloring of its dual. However, non-vertex coloring problems...

In graph theory, a nowhere-zero flow or NZ flow is a network flow that is nowhere zero. It is intimately connected (by duality) to coloring planar graphs...

In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal...

major second can be found half way the major third. The Tonnetz is the dual graph of Schoenberg's chart of the regions, and of course vice versa. Research...

Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...

The join graphs and join trees of a constraint satisfaction problem are graphs representing its dual problem or a problem obtained from the dual problem...

operation) is a graph operation defined on regular polyhedral graphs with degree 3 or 4. It also applies to the dual graph of these graphs, i.e. graphs with triangular...

involved in a constraint is called the constraint scope. The dual constraint graph is the graph in which the vertices are all constraint scopes involved in...

the graph. Edge connectivity is the dual concept to girth, the length of the shortest cycle in a graph, in the sense that the girth of a planar graph is...