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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 Errera graph ： ウィキペディア英語版 Errera graph In the mathematical field of graph theory, the Errera graph is a graph with 17 vertices and 45 edges discovered by Alfred Errera. Published in 1921, it provides an example of how Kempe's proof of the four color theorem cannot work.〔Errera, A. "Du coloriage des cartes et de quelques questions d'analysis situs." Ph.D. thesis. 1921.〕〔Peter Heinig. (Proof that the Errera Graph is a narrow Kempe-Impasse ). 2007.〕 Later, the Fritsch graph and Soifer graph provide two smaller counterexamples.〔Gethner, E. and Springer, W. M. II. "How False Is Kempe's Proof of the Four-Color Theorem?" Congr. Numer. 164, 159-175, 2003.〕 The Errera graph is planar and has chromatic number 4, chromatic index 6, radius 3, diameter 4 and girth 3. All its vertices are of degree 5 or 6 and it is a 5-vertex-connected graph and a 5-edge-connected graph. ==Algebraic properties== The Errera graph is not a vertex-transitive graph and its full automorphism group is isomorphic to the dihedral group of order 20, the group of symmetries of a decagon, including both rotations and reflections. The characteristic polynomial of the Errera graph is $-(x^2-2\; x-5)\; (x^2+x-1)^2\; (x^3-4\; x^2-9\; x+10)\; (x^4+2\; x^3-7\; x^2-18\; x-9)^2$. 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「Errera 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.