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GraphTheory

  

DrawPlanar

  

draw a planar graph stored in the Graph data structure

 

Calling Sequence

Parameters

Description

Examples

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

withGraphTheory:

withSpecialGraphs:

G1GraphTrail1,2,3,4,5,6,7,8,9,10,1,Trail11,12,6,11,1,12

G1Graph 1: an undirected unweighted graph with 12 vertices and 15 edge(s)

(1)

DrawPlanarG1

G2SoccerBallGraph

G2Graph 2: an undirected unweighted graph with 60 vertices and 90 edge(s)

(2)

DrawPlanarG2

See Also

DrawGraph