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Preprint
The Spark of Symmetric Matrices Described by a Graph
ArXiv.org
01 Jul 2023
Abstract
We investigate the sparsity of null vectors of real symmetric matrices whose off-diagonal pattern of zero and nonzero entries is described by the adjacencies of a graph. We use the definition of the spark of a matrix, the smallest number of nonzero coordinates of any null vector, to define the spark of a graph as the smallest possible spark of a corresponding matrix. We study connections of graph spark to well-known concepts including minimum rank, forts, orthogonal representations, Parter and Fiedler vertices, and vertex connectivity.
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Details
- Title
- The Spark of Symmetric Matrices Described by a Graph
- Creators
- Louis Deaett - Quinnipiac UniversityShaun Fallat - University of ReginaVeronika Furst - Fort Lewis CollegeJohn Hutchens - University of San FranciscoLon Mitchell - Eastern Michigan UniversityYaqi Zhang - Drexel University
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861307204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics