The rigidity of graphs, II
The rigidity of graphs, II
复制标题
DOI：
10.1016/0022-247x(79)90108-2
复制
发表时间：
1979-03
影响因子：
1.3
通讯作者：
L. Asimow;B. Roth
中科院分区：
文献类型：
--
作者：
L. Asimow;B. Roth
我们把图G看作一个集合{1，…，v}以及{1，…}的二元子集的非空集E、v}。设p=(p 1，…图G(P)是RnV的一个元素，表示Rn中的v个点，并考虑G(P)在Rn中的实现G(P)，G(P)由Rn中的线段[pi，pj]组成，对于{i，j}ϵE。如果RnV中的每条连续路径从p开始并保持G(P)的边长，终止于作为图像(Tp1，…)的点qϵRnv，则图G(P)在Rn中是刚性的本文研究了图、曲面以及更一般的结构的刚性和无穷小刚性。讨论了R2中确定图的刚性的图论方法，并考察了R3中凸多面体曲面的刚性。
We regard a graph G as a set {1,…, v} together with a nonempty set E of two-element subsets of {1,…, v}. Let p=(p 1,…, p v) be an element of R nv representing v points in R n and consider the realization G (p) of G in R n consisting of the line segments [p i, p j] in R n for {i, j} ϵ E. The figure G (p) is said to be rigid in R n if every continuous path in R nv, beginning at p and preserving the edge lengths of G (p), terminates at a point q ϵ R nv which is the image (Tp 1,…, Tp v) of p under an isometry T of R n. We here study the rigidity and infinitesimal rigidity of graphs, surfaces, and more general structures. A graph theoretic method for determining the rigidity of graphs in R 2 is discussed, followed by an examination of the rigidity of convex polyhedral surfaces in R 3.