The 2-dimensional rigidity of certain families of graphs

@article{Jackson2007The2R,
  title={The 2-dimensional rigidity of certain families of graphs},
  author={Bill Jackson and Brigitte Servatius and Herman Servatius},
  journal={Journal of Graph Theory},
  year={2007},
  volume={54},
  pages={154-166}
}
Laman’s characterization of minimally rigid 2-dimensional generic frameworks gives a matroid structure on the edge set of the underlying graph, as was first pointed out and exploited by L. Lovász and Y. Yemini. Global rigidity has only recently been characterized by a combination of two results due to T. Jordán and the first named author, and R. Connelly, respectively. We use these characterizations to investigate how graph theoretic properties such as transitivity, connectivity and regularity… CONTINUE READING