Gain-sparsity and symmetry-forced rigidity in the plane

DOI10.1007/s00454-015-9755-1zbMath1366.52021OpenAlexW2266634616WikidataQ36568826 ScholiaQ36568826MaRDI QIDQ262309

Shin-ichi Tanigawa, Tibor Jordán, Viktória E. Kaszanitzky

Publication date: 29 March 2016

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-015-9755-1

zbMATH Keywords

rotation symmetrydihedral symmetryframe matroidsgroup-labeled graphsinfinitesimal rigidityplanar bar-and-joint frameworksrigidity matroidsrigidity of graphssymmetry-forced rigidity

Mathematics Subject Classification ID

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

Related Items

Symmetry-forced rigidity of frameworks on surfaces ⋮ Matroids of gain graphs in applied discrete geometry ⋮ Rigidity of Frameworks on Expanding Spheres ⋮ Generic Symmetry-Forced Infinitesimal Rigidity: Translations and Rotations ⋮ Equivalence of continuous, local and infinitesimal rigidity in normed spaces ⋮ \(\ell^1\) and \(\ell^\infty\) plane ⋮ Frameworks with forced symmetry. I: Reflections and rotations ⋮ Pairing symmetries for Euclidean and spherical frameworks ⋮ Global rigidity of periodic graphs under fixed-lattice representations ⋮ Rigidity of symmetric frameworks in normed spaces ⋮ Motions of grid-like reflection frameworks ⋮ Symbol functions for symmetric frameworks ⋮ Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks ⋮ Flexible placements of graphs with rotational symmetry ⋮ Sufficient connectivity conditions for rigidity of symmetric frameworks ⋮ Inductive constructions for frameworks on a two-dimensional fixed torus ⋮ Gain-sparsity and symmetry-forced rigidity in the plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gain-sparsity and symmetry-forced rigidity in the plane
• Symmetry-forced rigidity of frameworks on surfaces
• Projective invariance of Shaky structures
• Symmetric versions of Laman's theorem
• The orbit rigidity matrix of a symmetric framework
• Biased graphs. I: Bias, balance, and gains
• Frameworks with forced symmetry. I: Reflections and rotations
• Simultaneous static and kinematic indeterminacy of space trusses with cyclic symmetry
• Biased graphs. II: The three matroids
• Count matroids of group-labeled graphs
• Connected rigidity matroids and unique realizations of graphs
• Group symmetry in interior-point methods for semidefinite program
• Generic combinatorial rigidity of periodic frameworks
• Inductive constructions for frameworks on a two-dimensional fixed torus
• Symmetry adapted assur decompositions
• Frameworks with forced symmetry. II: Orientation-preserving crystallographic groups
• Pebble game algorithms and sparse graphs
• Periodic frameworks and flexibility
• Symmetry as a Sufficient Condition for a Finite Flex
• FRAMEWORKS SYMMETRY AND RIGIDITY
• Matroids of gain graphs in applied discrete geometry
• Infinitesimal Rigidity of Symmetric Bar-Joint Frameworks
• Algorithms - ESA 2003