Rigid linkages and partial zero forcing
Combinatorics
2018-08-17 v1
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.
Keywords
Cite
@article{arxiv.1808.05553,
title = {Rigid linkages and partial zero forcing},
author = {Daniela Ferrero and Mary Flagg and H. Tracy Hall and Leslie Hogben and Jephian C. -H. Lin and Seth Meyer and Shahla Nasserasr and Bryan Shader},
journal= {arXiv preprint arXiv:1808.05553},
year = {2018}
}
Comments
23 pages