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A super stable tensegrity introduced by Connelly in 1982 is a globally rigiddiscrete structure made from stiff bars or struts connected by cables withtension. In this paper we show an exact relation between the maximum dimensionthat a multigraph can be realized as a super stable tensegrity and Colin deVerdi\`{e}re number~$\nu$ from spectral graph theory. As a corollary we obtaina combinatorial characterization of multigraphs that can be realized as3-dimensional super stable tensegrities.

Super Stable Tensegrities and Colin de Verdi\`{e}re Number $\nu$