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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 Cayley graph ： ウィキペディア英語版 Cayley graph In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley) and uses a specified, usually finite, set of generators for the group. It is a central tool in combinatorial and geometric group theory. == Definition == Suppose that $G$ is a group and $S$ is a generating set. The Cayley graph $\backslash Gamma=\backslash Gamma(G,S)$ is a colored directed graph constructed as follows: 〔 In his Collected Mathematical Papers 10: 403–405.〕 * Each element $g$ of $G$ is assigned a vertex: the vertex set $V(\backslash Gamma)$ of $\backslash Gamma$ is identified with $G.$ * Each generator $s$ of $S$ is assigned a color $c\_s$. * For any $g\backslash in\; G,\; s\backslash in\; S,$ the vertices corresponding to the elements $g$ and $gs$ are joined by a directed edge of colour $c\_s.$ Thus the edge set $E(\backslash Gamma)$ consists of pairs of the form $(g,\; gs),$ with $s\backslash in\; S$ providing the color. In geometric group theory, the set $S$ is usually assumed to be finite, symmetric (i.e. $S=S^$) and not containing the identity element of the group. In this case, the uncolored Cayley graph is an ordinary graph: its edges are not oriented and it does not contain loops (single-element cycles). 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「Cayley 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.