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Pentagonal Icositetrahedral Graph


PentagonalIcositetrahedralGraph

The pentagonal icositetrahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal icositetrahedron. It is implemented in the Wolfram Language as GraphData["PentagonalIcositetrahedralGraph"].

PentagonalIcositetrahedralGraphMatrices

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 order24
characteristic polynomial(x-2)^2(x-1)^3x(x^2-x-7)(x^2+x-3)(x^2+2x-1)^2(x^3-4x+1)^3(x^5+x^4-8x^3-9x^2+7x+4)^3
chromatic number3
chromatic polynomial?
claw-freeno
clique number2
determined by spectrum?
diameter7
distance-regular graphno
dual graph namesnub cubical graph
edge chromatic number4
edge connectivity3
edge count60
Eulerianno
girth5
Hamiltonianyes
Hamiltonian cycle count1452
Hamiltonian path count?
integral graphno
independence number16
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namespentagonal icositetrahedron
radius6
regularno
square-freeyes
traceableyes
triangle-freeyes
vertex connectivity3
vertex count38

See also

Archimedean Dual Graph, Pentagonal Icositetrahedron

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Pentagonal Icositetrahedral Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PentagonalIcositetrahedralGraph.html

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