On the Minimum Semidefinite Rank of a Simple Graph
0308-1087 (Print) 1563-5139 (Online)
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.
Taylor & Francis
Booth, M., Hackney, P., Harris, B., Johnson, C. R., Lay, M., Lenker, T. D., Mitchell, L. H., Narayan, S. K., Pascoe, A. & Sutton, B. D. (2011). On the minimum semidefinite rank of a simple graph. Linear and Multilinear Algebra, 59(5), 483-506. https://doi.org/10.1080/03081080903542791.