# DualPlanarGraph

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.
• • 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

open allclose all

## 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: