翻訳と辞書 Words near each other ・ Lamar Towers ・ Lamar Township ・ Lamaing, Ye ・ Lamak Mahalleh-ye Lafmejan ・ Lamakaan ・ Lamakun ・ Lamalera language ・ Lamalginite ・ Lamalif ・ Lamaline ・ Lamaling Monastery ・ Lamaload Reservoir ・ Lamalou-les-Bains ・ Laman (disambiguation) ・ Laman and Lemuel ・ Laman graph ・ Laman Tun Sri Lanang ・ Laman, Azerbaijan ・ Laman, Khachmaz ・ Laman, Lerik ・ Lamana Hotel ・ Lamanai ・ Lamancine ・ Lamanda Park (Pacific Electric) ・ Lamanda Park, Pasadena, California ・ Lamandau Nature Reserve ・ Lamandau Regency ・ Lamandau River ・ Lamane ・ Lamane Jegan Joof Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Laman graph ： ウィキペディア英語版 Laman graph In graph theory, the Laman graphs are a family of sparse graphs describing the minimally rigid systems of rods and joints in the plane. Formally, a Laman graph is a graph on ''n'' vertices such that, for all ''k'', every ''k''-vertex subgraph has at most 2''k'' − 3 edges, and such that the whole graph has exactly 2''n'' − 3 edges. Laman graphs are named after Gerard Laman, of the University of Amsterdam, who in 1970 used them to characterize rigid planar structures.〔.〕 ==Rigidity== Laman graphs arise in rigidity theory: if one places the vertices of a Laman graph in the Euclidean plane, in general position, there will in general be no simultaneous motion of all the points, other than Euclidean congruences, that preserves the lengths of all the graph edges. A graph is rigid in this sense if and only if it has a Laman subgraph that spans all of its vertices. Thus, the Laman graphs are exactly the minimally rigid graphs, and they form the bases of the two-dimensional rigidity matroids. If ''n'' points in the plane are given, then there are 2''n'' degrees of freedom in their placement (each point has two independent coordinates), but a rigid graph has only three degrees of freedom (the position of a single one of its vertices and the rotation of the remaining graph around that vertex). Intuitively, adding an edge of fixed length to a graph reduces its number of degrees of freedom by one, so the 2''n'' − 3 edges in a Laman graph reduce the 2''n'' degrees of freedom of the initial point placement to the three degrees of freedom of a rigid graph. However, not every graph with 2''n'' − 3 edges is rigid; the condition in the definition of a Laman graph that no subgraph can have too many edges ensures that each edge contributes to reducing the overall number of degrees of freedom, and is not wasted within a subgraph that is already itself rigid due to its other edges. 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「Laman 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.