The minimum rank problem over finite fields
Abstract
Description
The structure of all graphs having minimum rank at most k over a finite field with q elements is characterized for any possible k and q. A strong connection between this characterization and polarities of projective geometries is explained. Using this connection, a few results in the minimum rank problem are derived by applying some known results from projective geometry.
23 pages, 5 figures, 1 Sage program
23 pages, 5 figures, 1 Sage program