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Triakis Tetrahedral Graph


TriakisTetrahedralGraph

The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is the graph square of the 4-sunlet graph. It is a 3-tree.

It is implemented in the Wolfram Language as GraphData["TriakisTetrahedralGraph"].

TriakisTetrahedralGraphMatrices

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^2-3x-9)(x^2+x-1)^3
chromatic number4
chromatic polynomial(x-3)^5(x-2)(x-1)x
claw-freeno
clique number4
determined by spectrumyes
diameter2
distance-regular graphno
dual graph nametruncated tetrahedral graph
edge chromatic number6
edge connectivity3
edge count18
Eulerianno
girth3
Hamiltonianyes
Hamiltonian cycle count12
Hamiltonian path count456
integral graphno
independence number4
line graphno
perfect matching graphno
planaryes
polyhedral graphyes
polyhedron embedding namestriakis tetrahedron
radius2
regularno
square-freeno
traceableyes
triangle-freeno
vertex connectivity3
vertex count8

See also

Archimedean Dual Graph, Triakis Tetrahedron

Explore with Wolfram|Alpha

Cite this as:

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

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