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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 Balaban 11-cage ： ウィキペディア英語版 Balaban 11-cage In the mathematical field of graph theory, the Balaban 11-cage or Balaban (3-11)-cage is a 3-regular graph with 112 vertices and 168 edges named after A. T. Balaban. The Balaban 11-cage is the unique (3-11)-cage. It was discovered by Balaban in 1973.〔Balaban, A. T. "Trivalent Graphs of Girth Nine and Eleven and Relationships Among the Cages." Rev. Roumaine Math. 18, 1033-1043, 1973.〕 The uniqueness was proved by McKay and Myrvold in 2003. The Balaban 11-cage is a Hamiltonian graph and can be constructed by excision from the Tutte 12-cage by removing a small subtree and suppressing the resulting vertices of degree two.〔Geoffrey Exoo & Robert Jajcay, Dynamic cage survey, Electr. J. Combin. 15 (2008)〕 It has chromatic number 3, chromatic index 3, radius 6, diameter 8 and girth 11. It is also a 3-vertex-connected graph and a 3-edge-connected graph. ==Algebraic properties== The characteristic polynomial of the Balaban 11-cage is : $(x-3)\; x^\; (x^2-6)^5\; (x^2-2)^\; (x^3-x^2-4\; x+2)^2\backslash cdot$ $\backslash cdot(x^3+x^2-6\; x-2)\; (x^4-x^3-6\; x^2+4\; x+4)^4\; (x^5+x^4-8\; x^3-6\; x^2+12\; x+4)^8$. The automorphism group of the Balaban 11-cage is of order 64.〔 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「Balaban 11-cage」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.