Rigid Linkages and Partial Zero Forcing

@article{Ferrero2019RigidLA,
  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 A. Meyer and S. Nasserasr and Bryan L. Shader},
  journal={Electron. J. Comb.},
  year={2019},
  volume={26},
  pages={2}
}
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… 

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References

SHOWING 1-10 OF 22 REFERENCES
Smith Normal Form and acyclic matrices
An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter
Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph
TLDR
Two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities, and are referred to as the Strong Spectral Property and the Strong Multiplicity Property.
Zero forcing sets and minimum rank of graphs
Graph minors. XXI. Graphs with unique linkages
Minimum Rank Problems
The Zero Forcing Number of Graphs
TLDR
The forcing number of various classes of graphs is studied, including graphs of large girth, $H-free graphs for a fixed bipartite graph $H$, random and pseudorandom graphs.
ON TWO CONJECTURES REGARDING AN INVERSE EIGENVALUE PROBLEM FOR ACYCLIC SYMMETRIC MATRICES
For a given acyclic graph G, an important problem is to characterize all of the eigenvalues over all symmetric matrices with graph G. Of particular interest is the connection between this standard
Minimum number of distinct eigenvalues of graphs
The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven
SPECTRAL GRAPH THEORY AND THE INVERSE EIGENVALUE PROBLEM OF A GRAPH
Spectral Graph Theory is the study of the spectra of certain matrices defined from a given graph, including the adjacency matrix, the Laplacian matrix and other related matrices. Graph spectra have
...
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