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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 Blanuša snarks ： ウィキペディア英語版 Blanuša snarks In the mathematical field of graph theory, the Blanuša snarks are two 3-regular graphs with 18 vertices and 27 edges. They were discovered by Croatian mathematician Danilo Blanuša in 1946 and are named after him.〔Blanuša, D., "Problem cetiriju boja." Glasnik Mat. Fiz. Astr. Ser. II. 1, 31-42, 1946.〕 When discovered, only one snark was known—the Petersen graph. As snarks, the Blanuša snarks are connected, bridgeless cubic graphs with chromatic index equal to 4. Both of them have chromatic number 3, diameter 4 and girth 5. They are non-hamiltonian but are hypohamiltonian.〔Eckhard Steen, "On Bicritical Snarks" Math. Slovaca, 1997.〕 ==Algebraic properties== The automorphism group of the first Blanuša snark is of order 8 and is isomorphic to the Dihedral group ''D''4, the group of symmetries of a square. The automorphism group of the second Blanuša snark is an abelian group of order 4 isomorphic to the Klein four-group, the direct product of the Cyclic group Z/2Z with itself. The characteristic polynomial of the first and the second Blanuša snark are respectively : :$(x-3)(x-1)^3(x+1)(x+2)(x^4+x^3-7x^2-5x+6)(x^4+x^3-5x^2-3x+4)^2\backslash$ :$(x-3)(x-1)^3(x^3+2x^2-3x-5)(x^3+2x^2-x-1)(x^4+x^3-7x^2-6x+7)(x^4+x^3-5x^2-4x+3).\backslash$ 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「Blanuša snarks」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.