arXiv:1207.3319 Abstract | arXiv Analytics

arXiv:1207.3319 [math.CO]Abstract References Reviews Resources

Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptions

Published 2012-07-13Version 1

In this paper we study the rank of planar rigidity matrix of 4-valent graphs, both in case of generic realizations and configurations in general position, under various connectivity assumptions on the graphs. For each case considered, we prove a lower bound and provide an example which shows the order of the bound we proved is sharp. This work is closed related to work in \cite{Luo:Rigidity} and answers some questions raised there.

Comments: 15 pages, 5 figures

Categories: math.CO

Subjects: 52C25, 05C50

Keywords: lower bound, connectivity assumptions, planar rigidity matrix, generic realizations, general position

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