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 -sided antiprism has vertices and edges. They are regular, polyhedral, and also Hamiltonian graphs.
Examples
The first graph in the sequence, the tetrahedral graph, has 4 verticies and 6 edges. The second, the octahedral graph, has 6 vertices and 12 edges. Later graphs in the sequence are named after the type of antiprism they correspond to:- 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
- ...
2 | 3 | 4 | 5 | 6 | 7 | 8 |
Although geometrically the star polygons also form the faces of a different sequence of antiprisms, the star antiprisms, they do not form a different sequence of graphs.
Related graphs
An antiprism graph is a special case of a circulant graph, Ci2n.Other infinite sequences of polyhedral graph formed in a similar way from polyhedra with regular-polygon bases include the prism graphs and wheel graphs. Other vertex-transitive polyhedral graphs include the Archimedean graphs.