Cuboctahedral Graph


The cuboctahedral graph is an Archimedean quartic symmetric graph on 12 nodes and 24 edges that is the skeleton of the cuboctahedron, as well as the uniform cubohemioctahedron and octahemioctahedron.

It is planar, has graph diameter 3, graph radius 3, and is Hamiltonian.

It is implemented in the Wolfram Language as GraphData["CuboctahedralGraph"].

The cuboctahedral graph is the line graph of the cubical graph.

It has chromatic number 3, and chromatic polynomial


The cuboctahedral graph is an integral graph with graph spectrum Spec(G)=(-2)^50^32^34^1. Its automorphism group has order |Aut(G)|=48.

The bipartite double graph of the cuboctahedral graph is the rolling polyhedron graph of the cube.

See also

Archimedean Graph, Cuboctahedron, Quartic Symmetric Graph

Explore with Wolfram|Alpha


Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 267, 1998.

Cite this as:

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

Subject classifications