Journal Article Sufficient conditions for the global rigidity of graphs

Tanigawa, Shin-ichi

113pp.123 - 140 , 2015-07 , Elsevier Inc.
We investigate how to find generic and globally rigid realizations of graphs in R(d) based on elementary geometric observations. Our arguments lead to new proofs of a combinatorial characterization of the global rigidity of graphs in R(2) by Jackson and JoRdán and that of body-bar graphs in R(d) recently shown by Connelly, JoRdán, and Whiteley. We also extend the 1-extension theorem and Connelly's composition theorem, which are main tools for generating globally rigid graphs in R(d). In particular we show that any vertex-redundantly rigid graph in R(d) is globally rigid in R(d), where a graph G=(V, E) is called vertex-redundantly rigid if G−v is rigid for any v∈V.

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