Minimum rank of skew-symmetric matrices described by a graph

作者：Allison Mary; Bodine Elizabeth; DeAlba Luz Maria; Debnath Joyati; DeLoss Laura; Garnett Colin; Grout Jason; Hogben Leslie; Im Bokhee; Kim Hana; Nair Reshmi; Pryporova Olga; Savage Kendrick; Shader Bryan^*; Wehe Amy Wangsness

来源：Linear Algebra and Its Applications, 2010, 432(10): 2457-2472.

DOI：10.1016/j.laa.2009.10.001

• Minimum rank
• Minimum skew rank
• Skew-symmetric matrix
• Matching
• Pfaffian
• Rank
• Graph
• Matrix

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.

• 出版日期2010-5-1