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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 2''n'' vertices and 4''n'' edges. They are regular, polyhedral (and therefore by necessity also 3-vertex-connected, vertex-transitive, and planar graphs), and also Hamiltonian graphs.〔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.〕 An antiprism graph is a special case of a circulant graph, Ci2''n''(2,1). The first graph in the sequence, the octahedral graph, has 6 vertices and 12 edges. Later graphs in the sequence may be named after the type of antiprism they correspond to: * 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 * ... Although geometrically the star polygons also form the faces of a different sequence of (self-intersecting) antiprisms, the star antiprisms, they do not form a different sequence of graphs. Other infinite sequences of polyhedral graph formed in a similar way from polyhedra with regular-polygon bases include the prism graphs (graphs of prisms) and wheel graphs (graphs of pyramids). Other vertex-transitive polyhedral graphs include the Archimedean graphs. == References== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Antiprism graph」の詳細全文を読む スポンサード リンク
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