On the global rigidity of tensegrity graphs

Garamvölgyi, Dániel

doi:10.1016/j.dam.2021.06.007

Discrete Applied Mathematics

2021

DOI: 10.1016/j.dam.2021.06.007

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On the global rigidity of tensegrity graphs

Dániel Garamvölgyi

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2024

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Super stable tensegrities and the Colin de Verdière number ν $\nu $

Oba,

Tanigawa

2024

Journal of Graph Theory

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A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars and struts connected by cables with tension. We introduce the super stability number of a multigraph as the maximum dimension that a multigraph can be realized as a super stable tensegrity, and show that it equals the Colin de Verdière number minus one. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as three‐dimensional super stable tensegrities. We also show that, for any fixed , there is an infinite family of 3‐regular graphs that can be realized as ‐dimensional injective super stable tensegrities.

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Super stable tensegrities and the Colin de Verdière number ν $\nu $

Oba,

Tanigawa

2024

Journal of Graph Theory

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On the global rigidity of tensegrity graphs

Cited by 1 publication

References 9 publications

Super stable tensegrities and the Colin de Verdière number ν $\nu $

Super stable tensegrities and the Colin de Verdière number ν $\nu $

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