It is a famous result of Lovász and Yemini that 6-connected graphs are rigid in the plane (Lovász and Yemini, 1982). This was recently improved by Jackson and Jordán (2009) who showed that 6-mixed connectivity is also sufficient for rigidity. Here we give sufficient graph connectivity conditions for both ‘forced symmetric’ and ‘incidentally symmetric’ infinitesimal rigidity in the plane.
This is the author’s version of a work that was accepted for publication in Physics Reports. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Combinatorics, 109, 2023 DOI: 10.1016/j.ejc.2022.103639
