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Disdyakis Dodecahedral Graph


DisdyakisDodecahedralGraph

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"].

DisdyakisDodecahedralGraphMatrices

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.

propertyvalue
automorphism group order48
characteristic polynomial(x-4)^3x^4(x+2)^6(x^2-2)^5(x^3-26x-48)
chromatic number3
chromatic polynomial?
claw-freeno
clique number3
determined by spectrumno
diameter4
distance-regular graphno
dual graph namegreat rhombicuboctahedral graph
edge chromatic number8
edge connectivity4
edge count72
Eulerianyes
girth3
Hamiltonianyes
Hamiltonian cycle count697824
Hamiltonian path count?
integral graphno
independence number12
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namesdisdyakis dodecahedron, Escher's solid
radius4
regularno
square-freeno
traceableyes
triangle-freeno
vertex connectivity4
vertex count26

See also

Archimedean Dual Graph, Disdyakis Dodecahedron

Explore with Wolfram|Alpha

Cite this as:

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

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