TR-2007-08

Rigid Tensegrity Labellings of Graphs

Tibor Jordán, András Recski, Zoltán Szabadka

Published in:
European Journal of Combinatorics Volume 30, Issue 8, November 2009, Pages 1887-1895

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 labelled as bars, cables, and struts, is called a tensegrity graph. It is said to be rigid in R^d if it has an infinitesimally rigid realization in R^d as a tensegrity framework.
 
We show that a graph can be labelled as a rigid tensegrity graph in R^d containing only cables and struts if and only if it is redundantly rigid in R^d. When d=2 we give an efficient combinatorial algorithm for finding a rigid cable-strut labelling. We also obtain some partial results on the characterization of rigid tensegrity graphs in R².

Bibtex entry:

@techreport{egres-07-08,

AUTHOR	=	{Jord{\'a}n, Tibor and Recski, Andr{\'a}s and Szabadka, Zolt{\'a}n},
TITLE	=	{Rigid Tensegrity Labellings of Graphs},
NOTE	=	{{\tt egres.elte.hu}},
INSTITUTION	=	{Egerv{\'a}ry Research Group, Budapest},
YEAR	=	{2007},
NUMBER	=	{TR-2007-08}

}