Rigid Linkages and Partial Zero Forcing

Authors

Daniella Ferrero, Texas State University
Mary Flagg, University of St. Thomas
H. Tracy Hall, New Vistas, LLC
Leslie Hogben, Iowa State University; American Institute of Mathematics
Jephian C.-H. Lin, Iowa State University
Seth A. Meyer, St. Norbert College
Shahla Nasserasr, Nova Southeastern UniversityFollow
Bryan Shader, University of Wyoming

Document Type

Article

Publication Date

8-16-2018

Publication Title

arXiv.org

Keywords

Linkage, Vital, Rigid, Zero forcing, Inverse eigenvalue problem

First Page

1

Last Page

23

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.

Additional Comments

NSF grant #: DMS 1128242

NSUWorks Citation

Ferrero, Daniella; 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 Faculty Articles. 255.
https://nsuworks.nova.edu/math_facarticles/255

ORCID ID

0000-0002-7093-0479

DOI

https://arxiv.org/abs/1808.05553