On the Minimum Semidefinite Rank of a Simple Graph

Authors

Mathew Booth
Philip Hackney
Benjamin Harris
Charles Johnson
Margaret Lay
Terry Lenker
Lon Mitchell, University of South Florida St. PetersburgFollow
Sivaram Narayan
Amanda Pascoe
Brian Sutton

SelectedWorks Author Profiles:

Lon Mitchell

Document Type

Article

Publication Date

2011

ISSN

0308-1087 (Print) 1563-5139 (Online)

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.

Publisher

Taylor & Francis

Recommended Citation

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.