English

The minimum rank problem over finite fields

Combinatorics 2008-01-22 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0801.2987,
  title  = {The minimum rank problem over finite fields},
  author = {Jason Grout},
  journal= {arXiv preprint arXiv:0801.2987},
  year   = {2008}
}

Comments

23 pages, 5 figures, 1 Sage program

R2 v1 2026-06-21T10:04:29.075Z