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 . Its automorphism group has order .
The bipartite double graph of the cuboctahedral graph is the rolling polyhedron graph of the cube.
See also
Archimedean Graph, Cuboctahedron, Quartic Symmetric Graph
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References
Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 267, 1998.
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Cuboctahedral Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CuboctahedralGraph.html