Linking \((n-2)\)-dimensional panels in \(n\)-space. I: \((k-1,k)\)-graphs and \((k-1,k)\)-frames
type: Item
instance of: scholarly article
title: Linking \((n-2)\)-dimensional panels in \(n\)-space. I: \((k-1,k)\)-graphs and \((k-1,k)\)-frames
zbMATH Open document ID: 0759.05083
DOI: 10.1007/BF01787636
published in: Graphs and Combinatorics
publication date: 1992-06-27T00:00:00Z
review text: An \((m,k)\)-graph is a graph satisfying \(f\leq mu-k\) for each subset of \(f\) edges on \(u\) nodes where \(u\) is sufficiently large, and with equality when \(f\) is the number of edges of the graph. A \((k-1,k)\)-frame is a structure generalizing an \((n-2,2)\)-framework in \(n\)-spaces, a structure consisting of a finite set of \((n-2)\)-dimensional panels in \(n\)-spaces and a set of rigid bars each joining a pair of panels using ball joints. The author proves that a graph is the underlying graph of an isostatic \((k-1,k)\)-frame if and only if it is a \((k-1,k)\)-graph.
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 25817
zbMATH Keywords: multigraphs
zbMATH Keywords: rigid structure
zbMATH Keywords: panels
author: Tiong Seng Tay
MaRDI profile type: Publication
cites work: Q4076414
cites work: Edge-Disjoint Spanning Trees of Finite Graphs
cites work: Q3327256
cites work: Q3694165
cites work: Linking (n-2)-dimensional panels in n-space. II: (n-2,2)-frameworks and body and Hinge structures
description: scientific article; zbMATH DE number 25817