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, Ci2n(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
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.