The disdyakis triacontahedral graph is Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as GraphData["DisdyakisTriacontahedralGraph"].
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 | 120 |
Characteristic polynomial | |
chromatic number | 3 |
chromatic polynomial | ? |
claw-free | no |
clique number | 3 |
determined by spectrum | no |
diameter | 6 |
distance-regular graph | no |
dual graph name | great rhombicosidodecahedral graph |
edge chromatic number | ? |
edge connectivity | 4 |
edge count | 180 |
Eulerian | yes |
girth | 3 |
Hamiltonian | yes |
Hamiltonian cycle count | ? |
Hamiltonian path count | ? |
integral graph | no |
independence number | ? |
line graph | ? |
line graph name | 5-wheel graph |
perfect matching graph | no |
planar | yes |
polyhedral graph | yes |
polyhedron embedding names | disdyakis triacontahedron |
radius | 6 |
regular | no |
square-free | no |
traceable | yes |
triangle-free | no |
vertex connectivity | 4 |
vertex count | 62 |