Geodesic
The minimum rank problem over finite fields
The electronic journal of linear algebra, Tome 20 (2010), pp. 691-716.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05C50, 05C75, 15A03, 05B25, 51E20
Keywords: minimum rank, symmetric matrix, finite field, projective geometry, polarity graph, bilinear symmetric form 
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Grout, Jason. The minimum rank problem over finite fields. The electronic journal of linear algebra, Tome 20 (2010), pp. 691-716. http://geodesic.mathdoc.fr/item/ELA_2010__20__a5/