Geodesic
Rigid linkages and partial zero forcing
Daniela Ferrero1 ; Mary Flagg2 ; H. Tracy Hall3 ; Leslie Hogben4 ; Jephian C.-H. Lin5 ; Seth A. Meyer6 ; Shahla Nasserasr7 ; Bryan Shader8
1Texas State University
2University of St. Thomas
3NewVistas, LLC
4Iowa State University and American Institute of Mathematics
5Iowa State University
6St. Norbert College
7Nova Southeastern University
8University of Wyoming
The electronic journal of combinatorics, Tome 26 (2019) no. 2
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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.
DOI : 10.37236/8097
Classification : 05C50, 15A18, 15B57
Mots-clés : vital linkages, zero forcing

Daniela Ferrero  1   ; Mary Flagg  2   ; H. Tracy Hall  3   ; Leslie Hogben  4   ; Jephian C.-H. Lin  5   ; Seth A. Meyer  6   ; Shahla Nasserasr  7   ; Bryan Shader  8

1 Texas State University
2 University of St. Thomas
3 NewVistas, LLC
4 Iowa State University and American Institute of Mathematics
5 Iowa State University
6 St. Norbert College
7 Nova Southeastern University
8 University of Wyoming 
@article{10_37236_8097,
     author = {Daniela Ferrero and Mary Flagg and H. Tracy Hall and Leslie Hogben and Jephian C.-H. Lin and Seth A. Meyer and Shahla Nasserasr and Bryan Shader},
     title = {Rigid linkages and partial zero forcing},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {2},
     doi = {10.37236/8097},
     zbl = {1416.05171},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8097/}
}
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%A Bryan Shader
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Daniela Ferrero; Mary Flagg; H. Tracy Hall; Leslie Hogben; Jephian C.-H. Lin; Seth A. Meyer; Shahla Nasserasr; Bryan Shader. Rigid linkages and partial zero forcing. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/8097

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