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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 Colin de Verdière graph invariant ： ウィキペディア英語版 Colin de Verdière graph invariant Colin de Verdière's invariant is a graph parameter $\backslash mu(G)$ for any graph ''G,'' introduced by Yves Colin de Verdière in 1990. It was motivated by the study of the maximum multiplicity of the second eigenvalue of certain Schrödinger operators.〔 ==Definition== Let $G=(V,E)$ be a loopless simple graph. Assume without loss of generality that $V=\backslash$. Then $\backslash mu(G)$ is the largest corank of any symmetric matrix $M=(M\_)\backslash in\backslash mathbb^$ such that: * (M1) for all $i,j$ with $i\backslash neq\; j$: if ''i'' and ''j'' are adjacent, and $M\_=0$ if ''i'' and ''j'' are nonadjacent; * (M2) ''M'' has exactly one negative eigenvalue, of multiplicity 1; * (M3) there is no nonzero matrix $X=(X\_)\backslash in\backslash mathbb^$ such that $MX=0$ and such that $X\_=0$ whenever $i=j$ or $M\_\backslash neq\; 0$.〔〔 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「Colin de Verdière graph invariant」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.