The skeleton of a trapezohedron may be termed a trapezohedral graph. -trapezohedral graphs are illustrated above for to 10 in circular embeddings with the two interior points corresponding to the trapezohedron apices. The case corresponds to the cubical graph.
The trapezohedral graphs are bipartite, Hamiltonian, perfect, planar, polyhedral, traceable, triangle-free, and uniquely colorable.
The -trapezohedral graph has the following property counts.
property | count |
cycle count | |
edge count | |
face count | |
Hamiltonian cycle count | |
Hamiltonian path count | |
path count | |
vertex count |