DualPlanarGraph

DualPlanarGraph[g]

gives the dual of the planar graph g.

Details and Options

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 (2021), DualPlanarGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

Text

Wolfram Research (2021), DualPlanarGraph, Wolfram Language function, https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

CMS

Wolfram Language. 2021. "DualPlanarGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DualPlanarGraph.html.

APA

Wolfram Language. (2021). DualPlanarGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DualPlanarGraph.html

BibTeX

@misc{reference.wolfram_2024_dualplanargraph, author="Wolfram Research", title="{DualPlanarGraph}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/DualPlanarGraph.html}", note=[Accessed: 26-May-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_dualplanargraph, organization={Wolfram Research}, title={DualPlanarGraph}, year={2021}, url={https://reference.wolfram.com/language/ref/DualPlanarGraph.html}, note=[Accessed: 26-May-2024 ]}