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Triakis Icosahedral Graph


TriakisIcosahedralGraph

The triakis icosahedral graph is Archimedean dual graph which is the skeleton of the triakis icosahedron. It is implemented in the Wolfram Language as GraphData["TriakisIcosahedralGraph"].

TriakisIcosahedralGraphMatrices

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 order120
characteristic polynomialx^8(x^2-5x-15)(x^2+x-3)^5(x^4-15x^2-20x+5)^3
chromatic number4
chromatic polynomial?
claw-freeno
clique number4
determined by spectrum?
diameter4
distance-regular graphno
dual graph nametruncated dodecahedral graph
edge chromatic number10
edge connectivity3
edge count90
Eulerianno
girth3
Hamiltonianno
Hamiltonian cycle count0
Hamiltonian path count0
integral graphno
independence number20
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namesgreat dodecahedron, great stellated dodecahedron, spikey, triakis icosahedron
radius3
regularno
square-freeno
traceableno
triangle-freeno
vertex connectivity3
vertex count32

See also

Archimedean Dual Graph, Triakis Icosahedron

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Triakis Icosahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TriakisIcosahedralGraph.html

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