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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 Hoffman graph ： ウィキペディア英語版 Hoffman graph In the mathematical field of graph theory, the Hoffman graph is a 4-regular graph with 16 vertices and 32 edges discovered by Alan Hoffman. Published in 1963, it is cospectral to the hypercube graph Q4.〔Hoffman, A. J. "On the Polynomial of a Graph." Amer. Math. Monthly 70, 30-36, 1963.〕〔van Dam, E. R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.〕 The Hoffman graph has many common properties with the hypercube Q4—both are Hamiltonian and have chromatic number 2, chromatic index 4, girth 4 and diameter 4. It is also a 4-vertex-connected graph and a 4-edge-connected graph. However, it is not distance-regular. ==Algebraic properties== The Hoffman graph is not a vertex-transitive graph and its full automorphism group is a group of order 48 isomorphic to the direct product of the symmetric group S4 and the cyclic group Z/2Z. The characteristic polynomial of the Hoffman graph is equal to :$(x-4)\; (x-2)^4\; x^6\; (x+2)^4\; (x+4)$ making it an integral graph—a graph whose spectrum consists entirely of integers. It is the same spectrum than the hypercube Q4. 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「Hoffman 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.