The disdyakis dodecahedral graph is Archimedean dual graph which is the skeleton of the disdyakis dodecahedron. It is implemented in the Wolfram Language as GraphData["DisdyakisDodecahedralGraph"].
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 | 48 |
characteristic polynomial | |
chromatic number | 3 |
chromatic polynomial | ? |
claw-free | no |
clique number | 3 |
determined by spectrum | no |
diameter | 4 |
distance-regular graph | no |
dual graph name | great rhombicuboctahedral graph |
edge chromatic number | 8 |
edge connectivity | 4 |
edge count | 72 |
Eulerian | yes |
girth | 3 |
Hamiltonian | yes |
Hamiltonian cycle count | 697824 |
Hamiltonian path count | ? |
integral graph | no |
independence number | 12 |
line graph | ? |
perfect matching graph | no |
planar | yes |
polyhedral graph | yes |
polyhedron embedding names | disdyakis dodecahedron, Escher's solid |
radius | 4 |
regular | no |
square-free | no |
traceable | yes |
triangle-free | no |
vertex connectivity | 4 |
vertex count | 26 |