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Trapezohedral Graph


TrapezohedralGraphs

The skeleton of a trapezohedron may be termed a trapezohedral graph. n-trapezohedral graphs are illustrated above for n=3 to 10 in circular embeddings with the two interior points corresponding to the trapezohedron apices. The case n=3 corresponds to the cubical graph.

The trapezohedral graphs are bipartite, Hamiltonian, perfect, planar, polyhedral, traceable, triangle-free, and uniquely colorable.

The n-trapezohedral graph has the following property counts.

propertycount
cycle count1/6(2n^4+13n^3+43n^2+68n+42)
edge count4n
face count2n
Hamiltonian cycle count(n+1)(n+2)
Hamiltonian path count2n(3n^2-7n+6)
path count1/(30)n(16n^5-55n^4+230n^3-305n^2+564n-150)
vertex count2(n+1)

See also

Cubical Graph, Trapezohedron

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Cite this as:

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

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