Lower bound for the rank of rigidity matrix of 4-valent graphs under various connectivity assumptions
Abstract
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 Luo:Rigidity and answers some questions raised there.
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