Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

2018

Journal or Book Title

arXiv

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.

Comments

This is a pre-print of the article Ferrero, Daniela, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Seth Meyer, Shahla Nasserasr, and Bryan Shader. "Rigid linkages and partial zero forcing." arXiv preprint arXiv:1808.05553 (2018). Posted with permission.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

Published Version

Share

COinS