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Truncated Icosahedral Graph

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TruncatedIcosahedralGraph

The truncated icosahedral graph is the cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated icosahedron. It is sometimes known as the buckminsterfullerene graph (Godsil and Royle 2001, p. 211). A number of embeddings are shown above. It is implemented in the Wolfram Language as GraphData["TruncatedIcosahedralGraph"].

It has graph spectrum

(-2)^5(1/2(1-sqrt(17)))^3(-1)^30^51^12^3(1/2(1+sqrt(17)))^33^1.
TruncatedIcosahedralGraphLCF

It is Hamiltonian with 2180 Hamiltonian cycles. It has a total of 16 distinct LCF notations (two of length three, three of length two, and 11 of length 1), illustrated above.

See also

Archimedean Graph, Truncated Icosahedron

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References

Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, p. 211, 2001.Kostant, B. "The Graph of the Truncated Icosahedron and the Last Letter of Galois." Notices Amer. Math. Soc. 42, 959-968, 1995.Read, R. C. and Wilson, R. J. An Atlas of Graphs. Oxford, England: Oxford University Press, p. 268, 1998.

Cite this as:

Weisstein, Eric W. "Truncated Icosahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatedIcosahedralGraph.html

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