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Disdyakis Triacontahedral Graph

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DisdyakisTriacontahedralGraph

The disdyakis triacontahedral graph is an Archimedean dual graph which is the skeleton of the disdyakis triacontahedron. It is implemented in the Wolfram Language as GraphData["DisdyakisTriacontahedralGraph"].

DisdyakisTriacontahedralGraphMatrices

The plots above show the adjacency matrices, incidence matrices, and graph distance matrices for the disdyakis triacontahedral graph.

The following table summarizes some properties of the graph.

propertyvalue
automorphism group order120
Characteristic polynomial(x-1)^4x^5(x+1)^4(x+2)^(10)(x+4)(x^2-5)^3(x^2-3)^4(x^2-4x-15)(x^2-4x+1)^5(x^4-21x^2-40x-16)^3
chromatic number3
chromatic polynomial?
claw-freeno
clique number3
determined by spectrumno
diameter6
distance-regular graphno
dual graph namegreat rhombicosidodecahedral graph
edge chromatic number?
edge connectivity4
edge count180
Eulerianyes
girth3
Hamiltonianyes
Hamiltonian cycle count?
Hamiltonian path count?
integral graphno
independence number?
line graph?
line graph name5-wheel graph
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namesdisdyakis triacontahedron
radius6
regularno
square-freeno
traceableyes
triangle-freeno
vertex connectivity4
vertex count62

See also

Archimedean Dual Graph, Disdyakis Triacontahedron

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References

House of Graphs. "Disdyakis Triacontahedral Graph." https://houseofgraphs.org/graphs/1041.

Referenced on Wolfram|Alpha

Disdyakis Triacontahedral Graph

Cite this as:

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

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