8 citations · 23 across the 5 of their papers we have counts for
5 papers · 1 filter
Universal Rigidity of Bar Frameworks via the Geometry of Spectrahedra
A. Y. Alfakih
A bar framework (G,p) in dimension r is a graph G whose vertices are points p^1,...,p^n in R^r and whose edges are line segments between pairs of these points. Two frameworks (G,p)…
Graph connectivity and universal rigidity of bar frameworks
A. Y. Alfakih
Let be a graph on nodes. In this note, we prove that if is -vertex connected, , then there exists a configuration in general position in $…
On stress matrices of chordal bar frameworks in general position
A. Y. Alfakih
A bar framework in R^r, denoted by G(p), is a simple connected graph G whose vertices are points p^1,...,p^n in R^r that affinely span R^r, and whose edges are line segments betwee…
On affine motions and bar frameworks in general position
A. Y. Alfakih, Yinyu Ye
A configuration p in r-dimensional Euclidean space is a finite collection of points (p^1,...,p^n) that affinely span R^r. A bar framework, denoted by G(p), in R^r is a simple graph…
Toward the Universal Rigidity of General Frameworks
Abdo Y. Alfakih, Nicole Taheri, Yinyu Ye
Let (G,P) be a bar framework of n vertices in general position in R^d, d <= n-1, where G is a (d+1)-lateration graph. In this paper, we present a constructive proof that (G,P) admi…