The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is the graph square of the 4-sunlet graph. It is a 3-tree.
It is implemented in the Wolfram Language as GraphData["TriakisTetrahedralGraph"].
The plots above show the adjacency, incidence, and graph distance matrices for the deltoidal hexecontahedral graph.
The following table summarizes some properties of the graph.
property | value |
automorphism group order | 24 |
characteristic polynomial | |
chromatic number | 4 |
chromatic polynomial | |
claw-free | no |
clique number | 4 |
determined by spectrum | yes |
diameter | 2 |
distance-regular graph | no |
dual graph name | truncated tetrahedral graph |
edge chromatic number | 6 |
edge connectivity | 3 |
edge count | 18 |
Eulerian | no |
girth | 3 |
Hamiltonian | yes |
Hamiltonian cycle count | 12 |
Hamiltonian path count | 456 |
integral graph | no |
independence number | 4 |
line graph | no |
perfect matching graph | no |
planar | yes |
polyhedral graph | yes |
polyhedron embedding names | triakis tetrahedron |
radius | 2 |
regular | no |
square-free | no |
traceable | yes |
triangle-free | no |
vertex connectivity | 3 |
vertex count | 8 |