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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 Kautz graph ： ウィキペディア英語版 Kautz graph The Kautz graph $K\_M^$ is a directed graph of degree $M$ and dimension $N+$ 1, which has $(M\; +1)M^$ vertices labeled by all possible strings $s\_0\; \backslash cdots\; s\_N$ of length $N\; +$ 1 which are composed of characters $s\_i$ chosen from an alphabet $A$ containing $M\; +\; 1$ distinct symbols, subject to the condition that adjacent characters in the string cannot be equal ($s\_i\; \backslash neq\; s\_$). The Kautz graph $K\_M^$ has $(M\; +\; 1)M^$ edges $\backslash \; \backslash \}\; \backslash ,$ It is natural to label each such edge of $K\_M^$ as $s\_0s\_1\; \backslash cdots\; s\_$, giving a one-to-one correspondence between edges of the Kautz graph $K\_M^$ and vertices of the Kautz graph $K\_M^$. Kautz graphs are closely related to De Bruijn graphs. == Properties == * For a fixed degree $M$ and number of vertices $V\; =\; (M\; +\; 1)\; M^N$, the Kautz graph has the smallest diameter of any possible directed graph with $V$ vertices and degree $M$. * All Kautz graphs have Eulerian cycles. (An Eulerian cycle is one which visits each edge exactly once-- This result follows because Kautz graphs have in-degree equal to out-degree for each node) * All Kautz graphs have a Hamiltonian cycle (This result follows from the correspondence described above between edges of the Kautz graph $K\_M^$ and vertices of the Kautz graph $K\_M^$; a Hamiltonian cycle on $K\_M^$ is given by an Eulerian cycle on $K\_M^$) * A degree-$k$ Kautz graph has $k$ disjoint paths from any node $x$ to any other node $y$. 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「Kautz 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.