PlaneDual - Maple Help
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GraphTheory

 PlaneDual
 construct plane dual of planar graph

 Calling Sequence PlaneDual(G, opts) PlaneDual(F, opts)

Parameters

 G - planar graph F - list of faces of a planar graph opts - (optional) one or more options as listed below

Options

 • multigraph = truefalse
 Specifies whether multiple edges should be included in the graph returned. If true, the result may be a multigraph. The default value, false, leaves only a single edge remaining in the output.
 • selfloops = truefalse
 Specifies whether self-loops should be included in the graph returned. If true, the result may contain self-loops. The default value, false, removes all self-loops from the output.

Description

 • PlaneDual returns the plane dual of a planar graph G, that is, a graph with faces of G as its vertices in which two vertices are adjacent if and only if they share an edge as faces of G.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{DrawGraph}\left(\mathrm{HypercubeGraph}\left(3\right),\mathrm{style}=\mathrm{spring}\right)$
 > $G≔\mathrm{PlaneDual}\left(\mathrm{HypercubeGraph}\left(3\right)\right)$
 ${G}{≔}{\mathrm{Graph 1: an undirected graph with 6 vertices and 12 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawGraph}\left(G,\mathrm{style}=\mathrm{spring}\right)$

Compatibility

 • The GraphTheory[PlaneDual] command was updated in Maple 2023.
 • The multigraph and selfloops options were introduced in Maple 2023.
 • For more information on Maple 2023 changes, see Updates in Maple 2023.