The Rigidity of Infinite Graphs II

Kitson, Derek and Power, Stephen (2022) The Rigidity of Infinite Graphs II. Graphs and Combinatorics, 38 (3). ISSN 0911-0119

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Official URL: https://doi.org/10.1007/s00373-022-02486-y

Abstract

Inductive constructions are established for countably infinite simple graphs which have minimally rigid locally generic placements in R^2. This generalises a well-known result of Henneberg for generically rigid finite graphs. Inductive methods are also employed in the determination of the infinitesimal flexibility dimension of countably infinite graphs associated with infinitely faceted convex polytopes in R^3. In particular, a generalisation of Cauchy's rigidity theorem is obtained.

Item Type:

Journal Article

Journal or Publication Title:

Graphs and Combinatorics

Additional Information:

The final publication is available at Springer via http://dx.doi.org/10.1007/s00373-022-02486-y

Uncontrolled Keywords:

/dk/atira/pure/subjectarea/asjc/2600/2614

Subjects:

?? INFINITE GRAPHSINFINITESIMAL RIGIDITYCAUCHY'S RIGIDITY THEOREMGRAPH RIGIDITYDISCRETE MATHEMATICS AND COMBINATORICSTHEORETICAL COMPUTER SCIENCE ??

Departments:

Faculty of Science and Technology > Mathematics and Statistics

ID Code:

167787

Deposited By:

ep_importer_pure

Deposited On:

21 Mar 2022 14:05

Refereed?:

Yes

Published?:

Published

Last Modified:

20 Sep 2023 01:50

URI:

https://eprints-dev.lancs.ac.uk/id/eprint/167787