Operations preserving the global rigidity of graphs and frameworks in the plane

T. Jordán, Zoltán Szabadka

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

A straight-line realization of (or a bar-and-joint framework on) graph G in Rd is said to be globally rigid if it is congruent to every other realization of G with the same edge lengths. A graph G is called globally rigid in Rd if every generic realization of G is globally rigid. We give an algorithm for constructing a globally rigid realization of globally rigid graphs in R2. If G is triangle-reducible, which is a subfamily of globally rigid graphs that includes Cauchy graphs as well as Grünbaum graphs, the constructed realization will also be infinitesimally rigid. Our algorithm relies on the inductive construction of globally rigid graphs which uses edge additions and one of the Henneberg operations. We also show that vertex splitting, which is another well-known operation in combinatorial rigidity, preserves global rigidity in R2.

Original languageEnglish
Pages (from-to)511-521
Number of pages11
JournalComputational Geometry: Theory and Applications
Volume42
Issue number6-7
DOIs
Publication statusPublished - Aug 2009

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Rigidity
Graph in graph theory
Framework
Congruent
Straight Line
Cauchy
Triangle
Vertex of a graph

Keywords

  • Gale transform
  • Globally rigid framework
  • Rigid graph
  • Vertex split

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mathematics
  • Control and Optimization
  • Geometry and Topology

Cite this

Operations preserving the global rigidity of graphs and frameworks in the plane. / Jordán, T.; Szabadka, Zoltán.

In: Computational Geometry: Theory and Applications, Vol. 42, No. 6-7, 08.2009, p. 511-521.

Research output: Contribution to journalArticle

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