Cubic Polyhedral Graph

A cubic polyhedral graph is a graph that is both cubic and polyhedral. The numbers of cubical polyhedral graphs on n=2, 4, ... nodes are 0, 1, 1, 2, 5, 14, 50, 233, 1249, ... (OEIS A000109).


The following table summarizes some named cubical polyhedral graphs and classes of graphs, some of which are illustrated above.

Tabulations of cubic polyhedral graphs are commonly limited to those that are triangle-free (e.g., Read and Wilson 1998). The numbers of 2n-node triangle-free cubic polyhedral graphs on n=1, 2, ... nodes are 0, 0, 0, 1, 1, 2, 5, 12, 34, (OEIS A000103).


The figure above illustrates triangle-free cubic polyhedral graphs up to 18 vertices, together with their notation in Read and Wilson (1998).

See also

Cubic Graph, Cubic Symmetric Graph, Polyhedral Graph, Simple Polyhedron

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Bowen, R. and Fisk, S. "Generation of Triangulations of the Sphere." Math. Comput. 21, 250-252, 1967.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, 1998.Sloane, N. J. A. Sequences A000103/M1423 and A000109/M1469 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Cubic Polyhedral Graph

Cite this as:

Weisstein, Eric W. "Cubic Polyhedral Graph." From MathWorld--A Wolfram Web Resource.

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