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On the minimum semidefinite rank of a simple graph |
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| Authors: | Matthew Booth Philip Hackney Benjamin Harris Charles R Johnson Margaret Lay Terry D Lenker |
| Institution: | 1. Department of Mathematics , Oberlin College , Oberlin, OH 44074, USA;2. Department of Mathematics , Purdue University , West Lafayette, IN, 47907-2067, USA;3. Department of Mathematics , Brown University , Providence, RI, 02912, USA;4. Department of Mathematics , College of William and Mary , Williamsburg, VA, 23187-8795, USA;5. Department of Mathematics and Computer Science , Grinnell College , Grinnell, IA, 50112-1690, USA;6. Department of Mathematics , Central Michigan University , Mount Pleasant, MI, 48859, USA |
| Abstract: | 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. |
| Keywords: | rank positive semidefinite graph of a matrix vector representation |