DisCoMath Seminar: Relating linkages to the inverse eigenvalue problem on a graph
Discrete & Computational Math Seminar (DisCoMath)
Relating linkages to the inverse eigenvalue problem on a graph
Dr. Bonnie Jacob
Associate Professor
Department of Science and Mathematics, NTID
Abstract:
In this talk, we will describe the results presented in Rigid linkages and partial zero forcing* by Ferrero et al. (2019). We will discuss linkages and rigid linkage forcing. We will also explore how these concepts relate to matrix eigenvalue multiplicities. *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. https://arxiv.org/abs/1808.05553
Speaker Bio:
Dr. Jacob is an Associate Professor in the Science and Mathematics Department at the National Technical Institute for the Deaf, Rochester Institute of Technology Her research interests include: Graph Theory, Zero Forcing, Graph Labeling Problems, Minimum Rank Problems, and Agent-based Modeling.
Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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Event Snapshot
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Who
Open to the Public
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