Jason Grout
Published 2008-01-18Version 1
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.
Comments: 23 pages, 5 figures, 1 Sage program
The minimum rank problem over the finite field of order 2: minimum rank 3
On the minimum rank of a graph over finite fields
Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields
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