The minimum rank problem over the finite field of order 2: Minimum rank 3

DOI10.1016/j.laa.2008.08.025zbMath1194.05080arXivmath/0612331OpenAlexW2037025104MaRDI QIDQ999773

Raphael Loewy, Jason Grout, Wayne W. Barrett

Publication date: 10 February 2009

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612331

zbMATH Keywords

symmetric matrixminimum rankforbidden subgraphrank 3field of two elements

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Structural characterization of families of graphs (05C75) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (8)

Subgraph complementation and minimum rank ⋮ The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample ⋮ Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph ⋮ Graphs with real algebraic co-rank at most two ⋮ Decompositions of minimum rank matrices ⋮ Zero forcing sets and the minimum rank of graphs ⋮ On minimum rank and zero forcing sets of a graph ⋮ On the minimum rank of a graph over finite fields

Uses Software

• Magma
• nauty
• SageMath

Cites Work

• The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample
• The minimum rank of symmetric matrices described by a graph: a survey
• The Magma algebra system. I: The user language
• On Fiedler's characterization of tridiagonal matrices over arbitrary fields
• Computation of minimal rank and path cover number for certain graphs
• A characterization of tridiagonal matrices
• Minimum-rank matrices with prescribed graph
• On minimal rank over finite fields
• Graphs whose minimal rank is two
• Graphs whose minimal rank is two: The finite fields case

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