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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Möbius–Kantor graph ： ウィキペディア英語版 Möbius–Kantor graph In the mathematical field of graph theory, the Möbius–Kantor graph is a symmetric bipartite cubic graph with 16 vertices and 24 edges named after August Ferdinand Möbius and Seligmann Kantor. It can be defined as the generalized Petersen graph ''G''(8,3): that is, it is formed by the vertices of an octagon, connected to the vertices of an eight-point star in which each point of the star is connected to the points three steps away from it. ==Möbius–Kantor configuration== (詳細はpolygons with ''p'' sides each, having the property that the vertices of one polygon lie on the lines through the edges of the other polygon, and vice versa. If so, the vertices and edges of these polygons would form a projective configuration. For ''p'' = 4 there is no solution in the Euclidean plane, but found pairs of polygons of this type, for a generalization of the problem in which the points and edges belong to the complex projective plane. That is, in Kantor's solution, the coordinates of the polygon vertices are complex numbers. Kantor's solution for ''p'' = 4, a pair of mutually-inscribed quadrilaterals in the complex projective plane, is called the Möbius–Kantor configuration. The Möbius–Kantor graph derives its name from being the Levi graph of the Möbius–Kantor configuration. It has one vertex per point and one vertex per triple, with an edge connecting two vertices if they correspond to a point and to a triple that contains that point. The configuration may also be described algebraically in terms of the abelian group $\backslash mathbb\_3\backslash times\; \backslash mathbb\_3$ with nine elements. This group has four subgroups of order three (the subsets of elements of the form $(i,0)$, $(i,i)$, $(i,2i)$, and $(0,i)$ respectively), each of which can be used to partition the nine group elements into three cosets of three elements per coset. These nine elements and twelve cosets form a configuration, the Hesse configuration. Removing the zero element and the four cosets containing zero gives rise to the Möbius–Kantor configuration. 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「Möbius–Kantor graph」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.