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.
Copyright Owner
The Authors
Copyright Date
2018
Language
en
File Format
application/pdf
Recommended Citation
Ferrero, Daniela; Flagg, Mary; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Meyer, Seth A.; Nasserasr, Shahla; and Shader, Bryan, "Rigid linkages and partial zero forcing" (2018). Mathematics Publications. 203.
https://lib.dr.iastate.edu/math_pubs/203
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.