Rigid Two-Dimensional Frameworks with Two Coincident Points
Rigid Two-Dimensional Frameworks with Two Coincident Points
复制标题
具有两个重合点的刚性二维框架
DOI：
10.1007/s00373-013-1390-0
复制
发表时间：
2014
影响因子：
0.7
通讯作者：
Viktória E. Kaszanitzky
中科院分区：
文献类型：
--
作者：
Zsolt Fekete;T. Jordán;Viktória E. Kaszanitzky
LetG= （V，E）是一个图，是两个不同的顶点。给出了一个具有无限刚体的二维杆节点框架（G,p）的存在性的充分必要条件，该框架中杆节点与杆节点的位置重合。我们还确定了相应的修正广义刚度矩阵在地基上的秩函数。这些结果导致了有效的算法，用于测试图是否具有相对于指定顶点对的这种重合实现，更一般地说，用于计算矩阵的秩。
LetG= (V,E) be a graph andbe two distinct vertices. We give a necessary and sufficient condition for the existence of an infinitesimally rigid two-dimensional bar-and-joint framework (G,p), in which the positions ofuandvcoincide. We also determine the rank function of the corresponding modified generic rigidity matroid on ground-setE. The results lead to efficient algorithms for testing whether a graph has such a coincident realization with respect to a designated vertex pair and, more generally, for computing the rank ofGin the matroid.