Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks

DOI10.1137/130947192zbMath1327.52039arXiv1308.6380OpenAlexW2150528797MaRDI QIDQ5499736

Bernd Schulze, Shin-ichi Tanigawa

Publication date: 31 July 2015

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.6380

zbMATH Keywords

symmetryframeworksframe matroidsgroup-labeled graphsinfinitesimal rigidityrigidity matroidsrigidity of graphs

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Planar graphs; geometric and topological aspects of graph theory (05C10) Combinatorial aspects of matroids and geometric lattices (05B35) Rigidity and flexibility of structures (aspects of discrete geometry) (52C25)

Related Items (13)

Symmetry-forced rigidity of frameworks on surfaces ⋮ Equivalence of continuous, local and infinitesimal rigidity in normed spaces ⋮ \(\ell^1\) and \(\ell^\infty\) plane ⋮ Pairing symmetries for Euclidean and spherical frameworks ⋮ The rigidity of a partially triangulated torus ⋮ Rigidity of symmetric frameworks in normed spaces ⋮ Motions of grid-like reflection frameworks ⋮ Symbol functions for symmetric frameworks ⋮ Symmetric isostatic frameworks with \(\ell^1\) or \(\ell^\infty\) distance constraints ⋮ The first-order flexibility of a crystallographic framework ⋮ Maxwell-Laman counts for bar-joint frameworks in normed spaces ⋮ Sufficient connectivity conditions for rigidity of symmetric frameworks ⋮ Gain-sparsity and symmetry-forced rigidity in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Gain-sparsity and symmetry-forced rigidity in the plane
• Linking rigid bodies symmetrically
• When is a symmetric pin-jointed framework isostatic?
• Symmetric versions of Laman's theorem
• Symmetric Laman theorems for the groups \(\mathcal C_2\) and \(\mathcal C_s\)
• The orbit rigidity matrix of a symmetric framework
• Frameworks with forced symmetry. I: Reflections and rotations
• Block-diagonalized rigidity matrices of symmetric frameworks and applications
• Rigidity of multi-graphs. I: Linking rigid bodies in n-space
• Biased graphs. II: The three matroids
• A symmetry extension of Maxwell's rule for rigidity of frames
• Symmetry-adapted equilibrium matrices
• Generic combinatorial rigidity of periodic frameworks
• On graphs and rigidity of plane skeletal structures
• FRAMEWORKS SYMMETRY AND RIGIDITY
• Matroids of gain graphs in applied discrete geometry
• Injective and non-injective realizations with symmetry
• The Rigidity of Graphs
• Generic Rigidity with Forced Symmetry and Sparse Colored Graphs

This page was built for publication: Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks