## On the minimum semidefinite rank of a simple graph

Matthew Booth, Philip Hackney, Benjamin Harris, Charles R. Johnson, Margaret Lay, Terry D. Lenker, Lon H. Mitchell, Sivaram K. Narayan, Amanda Pascoe, and Brian D. Sutton

*Linear Multilinear Algebra* 59 (2011), no. 5, 483–506.
The minimum semidefinite rank of a graph is defined to be the minimum rank
among all positive semidefinite matrices whose zero/nonzero pattern corresponds to that
graph. We recall some known facts and present new results, including results concerning
the effects of vertex or edge removal from a graph on minimum semidefinite rank.

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