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
Brian D. Sutton


The minimum semidefinite rank (msr) 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 msr.