Minimum rank of skew-symmetric matrices described by a graph
| Autor: | Hana Kim, Bokhee Im, Olga Pryporova, Jason Grout, Mary Allison, Kendrick Savage, Elizabeth Bodine, Joyati Debnath, Colin Garnett, Reshmi Nair, Bryan L. Shader, Leslie Hogben, Luz Maria DeAlba, Laura DeLoss, Amy Wangsness Wehe |
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| Jazyk: | angličtina |
| Předmět: |
Matching (graph theory)
Skew-symmetric matrix Circuit rank Pfaffian 010103 numerical & computational mathematics 01 natural sciences Graph Combinatorics Matrix (mathematics) Discrete Mathematics and Combinatorics Rank (graph theory) Matching 0101 mathematics Mathematics Discrete mathematics Numerical Analysis Algebra and Number Theory Matrix 010102 general mathematics Minimum rank Rank Cycle rank Graph (abstract data type) Geometry and Topology Minimum skew rank |
| Zdroj: | Linear Algebra and its Applications. (10):2457-2472 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2009.10.001 |
| Popis: | The minimum (symmetric) rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. The problem of determining minimum (symmetric) rank has been studied extensively. We define the minimum skew rank of a simple graph G to be the smallest possible rank among all skew-symmetric matrices over F whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We apply techniques from the minimum (symmetric) rank problem and from skew-symmetric matrices to obtain results about the minimum skew rank problem. |
| Databáze: | OpenAIRE |
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