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# Antiprism graph

In the mathematical field of graph theory, an antiprism graph is a graph that has one of the antiprisms as its skeleton. An n-sided antiprism has 2n vertices and 4n edges. They are regular, polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, and planar graphs), and also Hamiltonian graphs.[1]

An antiprism graph is a special case of a circulant graph, Ci_{2n }(2,1).

Octahedral graph – 6 vertices, 12 edges

square antiprismatic graph – 8 vertices, 16 edges

Pentagonal antiprismatic graph – 10 vertices, 20 edges

Hexagonal antiprismatic graph – 12 vertices, 24 edges

Heptagonal antiprismatic graph – 14 vertices, 28 edges

Octagonal antiprismatic graph – 16 vertices, 32 edges

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There are also related star polygon antiprisms:

Pentagrammic antiprismatic graph – 10 vertices, 20 edges

Pentagrammic crossed-antiprismatic graph – 10 vertices, 20 edges

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See also

Regular map (graph theory)

Archimedean graph

Prism graph

Wheel graph

References

Read, R. C. and Wilson, R. J. An Atlas of Graphs, Oxford, England: Oxford University Press, 2004 reprint, Chapter 6 special graphs pp. 261, 270.

External links

Weisstein, Eric W., "Antiprism graph", MathWorld.

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

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