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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 Ultrahomogeneous graph ： ウィキペディア英語版 Ultrahomogeneous graph In mathematics, a ''k''-ultrahomogeneous graph is a graph in which every isomorphism between two of its induced subgraphs of at most ''k'' vertices can be extended to an automorphism of the whole graph. If a graph is 5-ultrahomogeneous, then it is ultrahomogeneous for every ''k''. The only finite connected graphs of this type are complete graphs, Turán graphs, 3 × 3 rook's graphs, and the 5-cycle. There are only two connected graphs that are 4-ultrahomogeneous but not 5-ultrahomogeneous: the Schläfli graph and its complement. The proof relies on the classification of finite simple groups.〔; ; .〕 The infinite Rado graph is countably ultrahomogeneous. ==Notes== 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「Ultrahomogeneous 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.