Cubic Planar Graphs

This page lists 3-connected cubic planar graphs. These can be found as the duals of the planar triangulations, and hence can be constructed very easily by using Brinkmann and McKay's program plantri.

Most graphs cannot be drawn nicely at all, but at least for planar graphs it is guaranteed that there is at least a drawing with no crossing edges. Therefore automatic drawing methods often focus on planar graphs. One such method is that described by Tutte, whereby the vertices of a face are placed on a regular polygon (of appropriate size) and the remaining vertices are placed according to the rule that each vertex (other than the fixed ones) is at the centroid of its neighbours. For these graphs, all such possible drawings have been calculated and can be viewed with a Java graph viewing applet.

The graphs themselves are available from the following table and as usual are in graph6 format.

Vertices	3-connected cubic planars
10	5
12	14
14	50
16	233
18	1249
20	7595

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Gordon Royle, gordon@cs.uwa.edu.au, January 1997