Please use this identifier to cite or link to this item: https://doi.org/10.1007/BF01787636
Title: Linking (n - 2)-dimensional panels in n-space I: (k - 1, k)-graphs and (k - 1, k)-frames
Authors: Tay, T.-S. 
Issue Date: Sep-1991
Citation: Tay, T.-S. (1991-09). Linking (n - 2)-dimensional panels in n-space I: (k - 1, k)-graphs and (k - 1, k)-frames. Graphs and Combinatorics 7 (3) : 289-304. ScholarBank@NUS Repository. https://doi.org/10.1007/BF01787636
Abstract: A (k - 1, k)-graph is a multi-graph satisfying e′ ≤ (k - 1)v′ - k for every non-empty subset of e′ edges on v′ vertices, with equality when e′ = |E(G)|. A (k - 1, k)-frame is a structure generalizing an (n - 2, 2)-framework in n-space, a structure consisting of a set of (n - 2)-dimensional bodies in n-space and a set of rigid bars each joining a pair of bodies using ball joints. We prove that a graph is the graph of a minimally rigid (with respect to edges) (k - 1, k)-frame if and only if it is a (k - 1, k)-graph. Rigidity here means infinitesimal rigidity or equivalently statical rigidity. © 1991 Springer-Verlag.
Source Title: Graphs and Combinatorics
URI: http://scholarbank.nus.edu.sg/handle/10635/103503
ISSN: 09110119
DOI: 10.1007/BF01787636
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