Sparks of symmetric matrices and their graphs

Authors

Louis Deaett, Quinnipiac University
Shaun Fallat, University of Regina, Canada
Veronika Furst, Fort Lewis College
John Hutchens, University of San Francisco
Lon Mitchell, Eastern Michigan University
Yaqi Zhang, Drexel University

Document Type

Article

Publication Date

2023

Department/School

Mathematics

Publication Title

Electronic Journal of Linear Algebra

Abstract

The spark of a matrix is the smallest number of nonzero coordinates of any nonzero null vector. For real symmetric matrices, the sparsity of null vectors is shown to be associated with the structure of the graph obtained from the off-diagonal pattern of zero and nonzero entries. The smallest possible spark of a matrix corresponding to a graph is defined as the spark of the graph. Connections are established between graph spark and well-known concepts including minimum rank, forts, orthogonal representations, Parter and Fiedler vertices, and vertex connectivity.

Comments

L. Mitchell is a faculty member in EMU's Department of Mathematics and Statistics

Link to Published Version

DOI: 10.13001/ela.2023.8025

Recommended Citation

Deaett, L., Fallat, S., Furst, V., Hutchens, J., Mitchell, L., & Zhang, Y. (2023). Sparks of symmetric matrices and their graphs. Electronic Journal of Linear Algebra, 39, 591–606. https://doi.org/10.13001/ela.2023.8025