Tóth Sára Hanna: Tensegrity frameworks

A realization of a graph $G$ in $d$-dimensional space is obtained from a simple graph $G$ by assigning a point $p(v)$ to each vertex $v$ of $G$. Each edge of $G$ corresponds to a line segment in the realization, connecting the points of the end-vertices of the edge. In some cases the edge lengths of the realization determine all pairwise distances, in the sense that every other realization of $G$ with the same edge lengths is a congruent copy. The goal is to study how this uniqueness property depends on $G$ and/or $p$.