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Pentagonal Hexecontahedral Graph

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PentagonalHexecontahedralGraph

The pentagonal hexecontahedral graph is the Archimedean dual graph which is the skeleton of the pentagonal hexecontahedron. It is implemented in the Wolfram Language as GraphData["PentagonalHexecontahedralGraph"].

PentagonalHexecontahedralGraphMatrices

The plots above show the adjacency matrix, incidence matrix, and graph distance matrix for the pentagonal hexecontahedral graph.

The following table summarizes some properties of the graph.

automorphism group order60
characteristic polynomial(x-2)^4(x-1)^5x^5(x+2)^4(x^2-x-8)(x^3-4x+2)^4(x^6-10x^4+21x^2-4x-4)^5(x^(10)+2x^9-17x^8-36x^7+83x^6+182x^5-119x^4-260x^3+60x^2+80x-20)^3
chromatic number3
chromatic polynomial?
claw-freeno
clique number2
determined by spectrum?
diameter10
distance-regular graphno
dual graph namesnub dodecahedral graph
edge chromatic number5
edge connectivity3
edge count150
Eulerianno
girth5
Hamiltonianyes
Hamiltonian cycle count?
Hamiltonian path count?
integral graphno
independence number?
line graph?
perfect matching graphno
planaryes
polyhedral graphyes
radius9
regularno
square-freeyes
traceableyes
triangle-freeyes
vertex connectivity3
vertex count92

See also

Archimedean Dual Graph, Pentagonal Hexecontahedron

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References

House of Graphs. "Pentagonal Hexecontahedral Graph." https://houseofgraphs.org/graphs/1257.

Referenced on Wolfram|Alpha

Pentagonal Hexecontahedral Graph

Cite this as:

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

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