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Uniformly
sparse graphs and matrices
Charles R. Johnson, Wenxuan Ding and Yuqiao Li |
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Vol. 17 (2024), No. 2, 249–262
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Abstract |
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The uniformly sparse (US) graphs, and the matrices associated with them, are introduced. These matrices have remarkable properties regarding diagonal equivalence and, thus, minimum rank. In the square case, this means that the determination of maximum geometric multiplicity of an eigenvalue is straightforward. Properties of US graphs, the matrices and the relationships with key parameters are discussed. |
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Keywords
directed graph, diagonal equivalence, minimum rank, path
cover number, tree, uniformly sparse matrix, zero forcing
number
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Mathematical Subject Classification
Primary: 05C50
Secondary: 15A18, 15A03, 05C20
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Milestones
Received: 26 February 2022
Revised: 1 July 2022
Accepted: 11 February 2023
Published: 20 May 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Charles R. Johnson | |
| Department of Mathematics The College of William & Mary Williamsburg, VA United States |
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| Wenxuan Ding | |
| Department of Mathematics The College of William & Mary Williamsburg, VA United States |
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| Yuqiao Li | |
| Department of Mathematics The College of William & Mary Williamsburg, VA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
