### Abstract

Tensegrity frameworks are defined on a set of points in R^{d} and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in R^{d} if every generic realization in R^{d} as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R^{1}.

Original language | English |
---|---|

Pages (from-to) | 1147-1149 |

Number of pages | 3 |

Journal | Discrete Applied Mathematics |

Volume | 161 |

Issue number | 7-8 |

DOIs | |

Publication status | Published - May 2013 |

### Fingerprint

### Keywords

- Graph
- NP-hard
- Rigidity
- Tensegrity framework

### ASJC Scopus subject areas

- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Applied Mathematics*,

*161*(7-8), 1147-1149. https://doi.org/10.1016/j.dam.2012.12.009

**Strongly rigid tensegrity graphs on the line.** / Jackson, Bill; Jordán, T.; Király, Csaba.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 161, no. 7-8, pp. 1147-1149. https://doi.org/10.1016/j.dam.2012.12.009

}

TY - JOUR

T1 - Strongly rigid tensegrity graphs on the line

AU - Jackson, Bill

AU - Jordán, T.

AU - Király, Csaba

PY - 2013/5

Y1 - 2013/5

N2 - Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.

AB - Tensegrity frameworks are defined on a set of points in Rd and consist of bars, cables, and struts, which provide upper and/or lower bounds for the distance between their endpoints. The graph of the framework, in which edges are labeled as bars, cables, and struts, is called a tensegrity graph. It is said to be strongly rigid in Rd if every generic realization in Rd as a tensegrity framework is infinitesimally rigid. In this note we show that it is NP-hard to test whether a given tensegrity graph is strongly rigid in R1.

KW - Graph

KW - NP-hard

KW - Rigidity

KW - Tensegrity framework

UR - http://www.scopus.com/inward/record.url?scp=84875225027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875225027&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2012.12.009

DO - 10.1016/j.dam.2012.12.009

M3 - Article

AN - SCOPUS:84875225027

VL - 161

SP - 1147

EP - 1149

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 7-8

ER -