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



Abstract

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 labelled as bars, cables, and struts, is called a tensegrity graph. It is said to be rigid in Rd if it has an infinitesimally rigid realization in Rd as a tensegrity framework.
 
We show that a graph can be labelled as a rigid tensegrity graph in Rd containing only cables and struts if and only if it is redundantly rigid in Rd. 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 www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2007},
NUMBER = {TR-2007-08}
}


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