On universally rigid frameworks on the line

T. Jordán, Viet Hang Nguyen

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A d-dimensional bar-and-joint framework (G; p) with underlying graph G is called universally rigid if all realizations of G with the same edge lengths, in all dimensions, are congruent to (G; p). We give a complete characterization of universally rigid one-dimensional bar-and-joint frameworks in general position with a complete bipartite underlying graph. We show that the only bipartite graph for which all generic d-dimensional realizations are universally rigid is the complete graph on two vertices, for all d ≥ 1. We also discuss several open questions concerning generically universally rigid graphs and the universal rigidity of general frameworks on the line.

Original languageEnglish
Pages (from-to)10-21
Number of pages12
JournalContributions to Discrete Mathematics
Volume10
Issue number2
Publication statusPublished - 2015

Fingerprint

Line
Complete Bipartite Graph
Congruent
Graph in graph theory
Complete Graph
Bipartite Graph
Rigidity
Framework

Keywords

  • Bar-and-joint framework
  • Bipartite framework
  • Cover graph
  • Generic rigidity
  • Global rigidity
  • Universal rigidity

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

On universally rigid frameworks on the line. / Jordán, T.; Nguyen, Viet Hang.

In: Contributions to Discrete Mathematics, Vol. 10, No. 2, 2015, p. 10-21.

Research output: Contribution to journalArticle

Jordán, T. ; Nguyen, Viet Hang. / On universally rigid frameworks on the line. In: Contributions to Discrete Mathematics. 2015 ; Vol. 10, No. 2. pp. 10-21.
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