LINKING (N-2)-DIMENSIONAL PANELS IN N-SPACE-I - (K-1,K)-GRAPHS AND (K-1,K)-FRAMES

A (k - 1, k)-graph is a multi-graph satisfying e' less-than-or-equal-to (k - 1)upsilon' - k for every non-empty subset of e' edges on upsilon' 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.