Minimum rank of skew-symmetric matrices described by a graph

By M. Allison, Elizabeth Milkovits, Luz M. DeAlba, J. Debnath, Laura DeLoss, C. Garnett, J. Grout, Leslie Hogben, Bokhee Im, Hana Kim and 5 more. 2010

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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 6= 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 6= 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.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f3c2fbf2f4d38ab90bb135a03ffb79e116bedb22