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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 Degree diameter problem ： ウィキペディア英語版 Degree diameter problem In graph theory, the degree diameter problem is the problem of finding the largest possible graph ''G'' (in terms of the size of its vertex set ''V'') of diameter ''k'' such that the largest degree of any of the vertices in ''G'' is at most ''d''. The size of ''G'' is bounded above by the Moore bound; for 1 < ''k'' and 2 < ''d'' only the Petersen graph, the Hoffman-Singleton graph, and maybe a graph of diameter ''k'' = 2 and degree ''d'' = 57 attain the Moore bound. In general the largest degree-diameter graphs are much smaller in size than the Moore bound. == Formula == Let $n\_$ be the maximum possible of vertices for a graph with degree at most ''d'' and diameter ''k'' then $n\_\backslash leq\; M\_$, where $M\_$ is the Moore bound: : This bound is attained for very few graphs, thus the study moves to how close there exist graphs to the Moore bound. For asymptotic behaviour note that $M\_=d^k+O(d^)$. Define the parameter $\backslash mu\_k=\backslash liminf\_\backslash frac$. It is conjectured that $\backslash mu\_k=1$ for all ''k''. It is known that $\backslash mu\_1=\backslash mu\_2=\backslash mu\_3=\backslash mu\_5=1$ and that $\backslash mu\_4\backslash geq\; 1/4$. For the general case it is known that $\backslash mu\_k\backslash geq\; 1.6^k$. Thus, although is conjectured that $\backslash mu\_k=1$ is still open if it is actually exponential. 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「Degree diameter problem」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.