Article
Rigid Linkages and Partial Zero Forcing
Electronic Journal of Combinatorics
Document Type
Article
Disciplines
Publication Version
Published Version
Publication Date
6-21-2019
DOI
10.37236/8097
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.
Creative Commons License
Creative Commons Attribution-No Derivative Works 4.0 International
Copyright Owner
The Authors
Copyright Date
2019
Language
en
File Format
application/pdf
Citation Information
Daniela Ferrero, Mary Flagg, H. Tracy Hall, Leslie Hogben, et al.. "Rigid Linkages and Partial Zero Forcing" Electronic Journal of Combinatorics Vol. 26 Iss. 2 (2019) p. P2.43 Available at: http://works.bepress.com/leslie-hogben/89/
This article is published as Ferrero, Daniela, Mary Flagg, H. Tracy Hall, Leslie Hogben, Jephian C-H. Lin, Seth A. Meyer, Shahla Nasserasr, and Bryan Shader. "Rigid Linkages and Partial Zero Forcing." The Electronic Journal of Combinatorics 26, no. 2 (2019): P2-43. DOI: 10.37236/8097. Posted with permission.