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 \cite{Luo:Rigidity} and answers some questions raised there.

15 pages, 5 figures

References in corpus (2)

• Lower Bound For The Rank Of 2-Dimensional Generic Rigidity Matroid For Regular Graphs Of Degree Four And Five
• On Graph Cohomology and Betti Numbers of Hamiltonian GKM Manifolds

Cited by in corpus (1)

• Lower Bound For The Rank Of 2-Dimensional Generic Rigidity Matroid For Regular Graphs Of Degree Four And Five