Infinitesimal rigidity for non-Euclidean bar-joint frameworks

Kitson, Derek and Power, Stephen (2014) Infinitesimal rigidity for non-Euclidean bar-joint frameworks. Bulletin of the London Mathematical Society, 46 (4). pp. 685-697. ISSN 0024-6093

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Abstract

The minimal innitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R2, ||.||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 lq 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.