DrawPlanar - Maple Help

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GraphTheory

 DrawPlanar
 draw a planar graph stored in the Graph data structure

 Calling Sequence DrawPlanar(G)

Parameters

 G - graph

Description

 • DrawPlanar displays the vertices and edges of a graph G as a Maple plot.
 • The algorithm used is Tutte's spring (or rubber) method. The vertices are placed on a face on a regular polygon, and the positions of the rest of the vertices are solved for such that each vertex is placed in the center of gravity of its neighbors.
 • Tutte's spring method works only for 3-connected graphs, so when the input graph is not 3-connected, strategies are employed to find a similar 3-connected graph (for example, 2-connected vertices are absorbed into the neighboring vertices).
 • The algorithm also finds a second drawing based on the first and chooses the one with the least "energy" for output.
 • Use of DrawPlanar can also be specified by a call to DrawGraph with option style=planar.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $\mathrm{G1}≔\mathrm{Graph}\left(\mathrm{Trail}\left(1,2,3,4,5,6,7,8,9,10,1\right),\mathrm{Trail}\left(11,12,6,11,1,12\right)\right)$
 ${\mathrm{G1}}{≔}{\mathrm{Graph 1: an undirected unweighted graph with 12 vertices and 15 edge\left(s\right)}}$ (1)
 > $\mathrm{DrawPlanar}\left(\mathrm{G1}\right)$
 > $\mathrm{G2}≔\mathrm{SoccerBallGraph}\left(\right)$
 ${\mathrm{G2}}{≔}{\mathrm{Graph 2: an undirected unweighted graph with 60 vertices and 90 edge\left(s\right)}}$ (2)
 > $\mathrm{DrawPlanar}\left(\mathrm{G2}\right)$

 See Also