Cubic Vertex-Transitive Graph


A cubic vertex-transitive graph is a cubic graph that is vertex transitive. Read and Wilson (1998, pp. 161-163) enumerate all connected cubic vertex-transitive graphs on 34 and fewer nodes, some of which are illustrated above. The numbers of such graphs on n=2, 4, 6, ... nodes are 0, 1, 2, 2, 3, 4, 3, 4, 5, 7, 3, 11, 5, 6, 10, 10, 5, ... (OEIS A032355).

The cubic symmetric graphs are a special case of the cubic vertex-transitive graphs (i.e., those that are also edge-transitive).

Classes of connected cubic vertex-transitive graphs include the prism graphs, even Möbius ladders, and crossed prism graphs. Specific cases are summarized in the following table.

See also

Crossed Prism Graph, Cubic Graph, Cubic Symmetric Graph, Quartic Vertex-Transitive Graph, Vertex-Transitive Graph

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Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, pp. 161-163, 1998.Sloane, N. J. A. Sequences A032355 in "The On-Line Encyclopedia of Integer Sequences."

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Cubic Vertex-Transitive Graph

Cite this as:

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

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