Orthogonal representations, minimum rank, and graph complements

DOI10.1016/j.laa.2007.12.004zbMath1147.05049OpenAlexW1993725206MaRDI QIDQ924328

Leslie Hogben

Publication date: 15 May 2008

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

Full work available at URL: https://lib.dr.iastate.edu/math_pubs/87

zbMATH Keywords

unicyclic graphminimum rank2-treegraph complementorthogonal representation

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (11)

Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph ⋮ On the graph complement conjecture for minimum rank ⋮ Graphs associated with vector spaces of even dimension: A link with differential geometry ⋮ The minimum semidefinite rank of the complement of partial \(k\)-trees ⋮ The minimum semidefinite rank of a triangle-free graph ⋮ The inverse inertia problem for the complements of partial \(k\)-trees ⋮ On the minimum semidefinite rank of a simple graph ⋮ A new graph parameter related to bounded rank positive semidefinite matrix completions ⋮ On minimum rank and zero forcing sets of a graph ⋮ Graph complement conjecture for classes of shadow graphs ⋮ On extremal graphs for zero forcing number

Cites Work

• Linearly independent vertices and minimum semidefinite rank
• Forbidden minors for the class of graphs \(G\) with \(\xi (G) \leqslant 2\)
• The minimum rank of symmetric matrices described by a graph: a survey
• Graphs whose positive semi-definite matrices have nullity at most two
• Computation of minimal rank and path cover number for certain graphs
• Zero forcing sets and the minimum rank of graphs
• Unitary matrix digraphs and minimum semidefinite rank
• On the difference between the maximum multiplicity and path cover number for tree-like graphs
• On the minimum semidefinite rank of a simple graph
• On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph
• Graphs whose minimal rank is two

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