DualPlanarGraph

DualPlanarGraph[g]

gives the dual of the planar graph g.

Details

  • DualPlanarGraph is also known as geometric dual graph and combinatorial dual graph.
  • DualPlanarGraph is typically used to associate dual structures such as flow and cellular networks, or Voronoi and Delaunay diagrams.
  • DualPlanarGraph[g] gives a graph that has a vertex for each face of g and an edge for each pair of faces separated from each other by an edge.
  • DualPlanarGraph takes the same options as Graph.

Examples

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Basic Examples  (2)

The dual of the planar graph:

The three-dimensional HypercubeGraph is planar:

Scope  (4)

DualPlanarGraph works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Applications  (1)

Find a partition of the vertices of the dual graph into two subsets whose induced subgraphs are both trees:

Find a Hamiltonian cycle:

The dual graph:

Select vertices contained in a Hamiltonian cycle:

Show induced subgraphs of partitions:

Properties & Relations  (2)

Use PlanarFaceList to get the faces of planar graphs:

Use FindPlanarColoring to find a coloring for the faces of planar graphs:

Possible Issues  (2)

DualPlanarGraph depends on faces based on the given layout:

DualPlanarGraph depends on faces based on the given coordinates:

Wolfram Research (13), DualPlanarGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

Text

Wolfram Research (13), DualPlanarGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

CMS

Wolfram Language. 13. "DualPlanarGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

APA

Wolfram Language. (13). DualPlanarGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DualPlanarGraph.html

BibTeX

@misc{reference.wolfram_2021_dualplanargraph, author="Wolfram Research", title="{DualPlanarGraph}", year="13", howpublished="\url{https://reference.wolfram.com/language/ref/DualPlanarGraph.html}", note=[Accessed: 24-January-2022 ]}

BibLaTeX

@online{reference.wolfram_2021_dualplanargraph, organization={Wolfram Research}, title={DualPlanarGraph}, year={13}, url={https://reference.wolfram.com/language/ref/DualPlanarGraph.html}, note=[Accessed: 24-January-2022 ]}