Small Rhombicuboctahedral Graph


The small rhombicuboctahedral graph is a quartic graph on 24 nodes and 48 edges that corresponds to the skeleton of the small rhombicuboctahedron. It has graph diameter 5, graph radius 5, and chromatic number 3. It is also Hamiltonian. It is vertex-transitive, although not edge-transitive because some edges are part of three-circuits while others are not.

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

It is the skeleton of the great cubicuboctahedron, great rhombicuboctahedron, great rhombihexahedron, quasirhombicuboctahedron, small cubicuboctahedron, small rhombicuboctahedron, small rhombihexahedron uniform polyhedra.

It has graph spectrum Spec(G)=(-3)^2[1/2(-1-sqrt(17))]^3(-1)^60^41^2[1/2(-1+sqrt(17))]^33^34^1. It automorphism group is of order |Aut(G)|=48.

See also

Quartic Graph, Small Rhombicuboctahedron

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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. "Small Rhombicuboctahedral Graph." From MathWorld--A Wolfram Web Resource.

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