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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 Asymmetric graph ： ウィキペディア英語版 Asymmetric graph In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism of a graph is a permutation ''p'' of its vertices with the property that any two vertices ''u'' and ''v'' are adjacent if and only if ''p''(''u'') and ''p''(''v'') are adjacent. The identity mapping of a graph onto itself is always an automorphism, and is called the trivial automorphism of the graph. An asymmetric graph is a graph for which there are no other automorphisms. ==Examples== The smallest asymmetric non-trivial graphs have 6 vertices.〔 The smallest asymmetric regular graphs have ten vertices; there exist ten-vertex asymmetric graphs that are 4-regular and 5-regular.〔.〕〔.〕 One of the two smallest asymmetric cubic graphs is the twelve-vertex Frucht graph discovered in 1939.〔.〕 According to a strengthened version of Frucht's theorem, there are infinitely many asymmetric cubic graphs. 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「Asymmetric 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.