Rigid linkages and partial zero forcing

Authors

Daniela Ferrero, Texas State UniversityFollow
Mary Flagg, University of St. ThomasFollow
H. Tracy Hall, New Vistas, LLCFollow
Leslie Hogben, Iowa State UniversityFollow
Seth A. Meyer, St. Norbert CollegeFollow
Jephian C.-H. Lin, Iowa State UniversityFollow
Shahla Nasserasr, Nova Southeastern UniversityFollow
Bryan Shader, University of WyomingFollow

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Description

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.

Publication Date

6-2019

Publisher

The Electronic Journal of Combinatorics

Keywords

Linkage, Vital, Rigid, Zero Forcing, Inverse Eigenvalue Problem

Comments

This article was originally published in The Electronic Journal of Combinatorics. The original article can be found here.

Recommended Citation

Ferrero, Daniela; Flagg, Mary; Hall, H. Tracy; Hogben, Leslie; Meyer, Seth A.; Lin, Jephian C.-H.; Nasserasr, Shahla; and Shader, Bryan, "Rigid linkages and partial zero forcing" (2019). Faculty Creative and Scholarly Works. 22.
https://digitalcommons.snc.edu/faculty_staff_works/22