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Tilley Graph


TilleyGraph

The Tilley graph is a polyhedral graph that arises in the investigation of Kempe chainsKempe Chain (Tilley 2018). It has 12 vertices, 29 edges, and 19 faces (one of which is a quadrilateral and the remainder of which are triangular). It can be constructed by removing any single edge from the icosahedral graph (E. Weisstein, Sep. 9, 2022).

There are 6 symmetrically distinct triangular faces out of the 18 total triangular faces.

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


See also

Icosahedral Graph, Kempe Chain

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References

Tilley, J. A. "Using Kempe Exchanges to Disentangle Kempe Chains." Math. Intel. 40, 50-54, 2018.

Cite this as:

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

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