Truncated Octahedral Graph


The truncated octahedral graph is the cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated octahedron. It is isomorphic to the Bruhat graph B_4, meaning it is the graph having have all permutations of {1,2,3,4} as vertices with an edge between pairs of permutations that differ by an adjacent transposition.

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

The truncated octahedral graph is vertex-transitive but not edge-transitive. It is Hamiltonian. It has LCF notations [3,-7,7,-3]^6, [5,-11,11,7,5,-5,-7,-11,11,-5,-7,7]^2, and [-11, 5, -3, -7, -9, 3, -5, 5, -3, 9, 7, 3, -5, 11, -3, 7, 5, -7, -9, 9, 7, -5, -7, 3].

It has graph spectrum Spec(G)=(+/-3)^1(+/-1)^3(+/-1+/-sqrt(2))^3(+/-sqrt(3))^2. Its automorphism group is of order |Aut(G)|=48.

See also

Archimedean Graph, Bruhat Graph, Truncated Octahedron

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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. "Truncated Octahedral Graph." From MathWorld--A Wolfram Web Resource.

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