Journal
LINEAR ALGEBRA AND ITS APPLICATIONS
Volume 432, Issue 10, Pages 2457-2472Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2009.10.001
Keywords
Minimum rank; Minimum skew rank; Skew-symmetric matrix; Matching; Pfaffian; Rank; Graph; Matrix
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Funding
- IMA
- NSF [DMS-0753009]
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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 not equal 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 not equal 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. (C) 2009 Elsevier Inc. All rights reserved.
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