Super Stable Tensegrities and the Colin de Verdi\`{e}re Number $\nu$
Combinatorics
2024-02-27 v2 Metric Geometry
Abstract
A super stable tensegrity introduced by Connelly in 1982 is a globally rigid discrete structure made from stiff bars or struts connected by cables with tension. In this paper we show an exact relation between the maximum dimension that a multigraph can be realized as a super stable tensegrity and Colin de Verdi\`{e}re number~ from spectral graph theory. As a corollary we obtain a combinatorial characterization of multigraphs that can be realized as 3-dimensional super stable tensegrities.
Keywords
Cite
@article{arxiv.2212.04556,
title = {Super Stable Tensegrities and the Colin de Verdi\`{e}re Number $\nu$},
author = {Ryoshun Oba and Shin-ichi Tanigawa},
journal= {arXiv preprint arXiv:2212.04556},
year = {2024}
}