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arXiv · 1808.05553

Rigid linkages and partial zero forcing

Daniela Ferrero·Mary Flagg·H. Tracy Hall·Leslie Hogben·Jephian C. -H. Lin·Seth Meyer·Shahla Nasserasr·Bryan Shader
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Abstract

Connections between vital linkages and zero forcing are established. Specifically, the notion of a rigid linkage is introduced as a special kind of unique linkage and it is shown that spanning forcing paths of a zero forcing process form a spanning rigid linkage and thus a vital linkage. A related generalization of zero forcing that produces a rigid linkage via a coloring process is developed. One of the motivations for introducing zero forcing is to provide an upper bound on the maximum multiplicity of an eigenvalue among the real symmetric matrices described by a graph. Rigid linkages and a related notion of rigid shortest linkages are utilized to obtain bounds on the multiplicities of eigenvalues of this family of matrices.

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Daniela Ferrero, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C. -H. Lin, Seth Meyer, Shahla Nasserasr, Bryan Shader. 2018-08-16. Rigid linkages and partial zero forcing. https://arxiv.org/abs/1808.05553

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