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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 Half-transitive graph ： ウィキペディア英語版 Half-transitive graph In the mathematical field of graph theory, a half-transitive graph is a graph that is both vertex-transitive and edge-transitive, but not symmetric. In other words, a graph is half-transitive if its automorphism group acts transitively upon both its vertices and its edges, but not on ordered pairs of linked vertices. Every connected symmetric graph must be vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree, so that half-transitive graphs of odd degree do not exist. However, there do exist half-transitive graphs of even degree.〔Bouwer, Z. "Vertex and Edge Transitive, But Not 1-Transitive Graphs." Canad. Math. Bull. 13, 231–237, 1970.〕 The smallest half-transitive graph is the Holt graph, with degree 4 and 27 vertices.〔.〕 ==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「Half-transitive 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.