Minimum rank with zero diagonal

Date
2014-06-01
Authors
Grood, Cheryl
Harmse, Johannes
Hogben, Leslie
Hogben, Leslie
Hunter, Thomas
Jacob, Bonnie
Klimas, Andrew
McCathern, Sharon
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Altmetrics
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Research Projects
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Mathematics
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Abstract

Associated with a simple graph G is a family of real, symmetric zero diagonal matrices with the same nonzero pattern as the adjacency matrix of G. The minimum of the ranks of the matrices in this family is denoted mr(0)(G). We characterize all connected graphs G with extreme minimum zero-diagonal rank: a connected graph G has mr(0)(G)

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<p>This article is published as Grood, Cheryl, Johannes Harmse, Leslie Hogben, Thomas Hunter, Bonnie Jacob, Andrew Klimas, and Sharon McCathern. "Minimum rank with zero diagonal." <em>The Electronic Journal of Linear Algebra</em> 27 (2014): 458-477. DOI: <a href="https://doi.org/10.13001/1081-3810.1630" target="_blank">10.13001/1081-3810.1630</a>. Posted with permission.</p>
Keywords
Zero-Diagonal, Minimum rank, Maximum nullity, Zero forcing number, Perfect [1, 2]-factor, Spanning generalized cycle, Matrix, Graph
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