Infinitesimal rigidity for non-Euclidean bar-joint frameworks

Abstract

The minimal infinitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R^2, ||.||_q) are characterised in terms of (2,2)-tight graphs. Specifically, a generically placed bar-joint framework (G,p) in the plane is minimally infinitesimally rigid with respect to a non-Euclidean l^q norm if and only if the underlying graph G = (V,E) contains 2|V|-2 edges and every subgraph H=(V(H),E(H)) contains at most 2|V(H)|-2 edges.