The minimum rank problem over finite fields

Details The minimum rank problem over finite fields The minimum rank problem over finite fields

2008-01-18

arxiv.org/abs/0801.2987v1

Mathematics

Combinatorics

23 pages, 5 figures, 1 Sage program

Scientific paper

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.

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