Minimum rank problems

DOI10.1016/j.laa.2009.05.003zbMath1213.05036OpenAlexW2093817461MaRDI QIDQ848577

Leslie Hogben

Publication date: 4 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.05.003

zbMATH Keywords

treegraphranksymmetric matrixmatrixpath coverminimum rankmaximum nullityzero forcing numberzero forcing setdirected treepath cover numberasymmetric minimum rankditreesymmetric minimum rank

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (27)

Subgraph complementation and minimum rank ⋮ On the zero forcing number and propagation time of oriented graphs ⋮ Using a new zero forcing process to guarantee the strong Arnold property ⋮ Unnamed Item ⋮ Extremal \(k\)-forcing sets in oriented graphs ⋮ Strong structural controllability of networks ⋮ An integer program for positive semidefinite zero forcing in graphs ⋮ Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph ⋮ A technique for computing the zero forcing number of a graph with a cut-vertex ⋮ On the minimum rank of the third power of a starlike tree ⋮ The zero forcing number of graphs with the matching number and the cyclomatic number ⋮ Almost full rank matrices arising from transitive tournaments ⋮ Propagation time for zero forcing on a graph ⋮ Zero forcing number, Grundy domination number, and their variants ⋮ Zero forcing in iterated line digraphs ⋮ Zero forcing number, constrained matchings and strong structural controllability ⋮ Optimal regulation of flow networks with transient constraints ⋮ A zero forcing technique for bounding sums of eigenvalue multiplicities ⋮ Zero forcing propagation time on oriented graphs ⋮ Rigid linkages and partial zero forcing ⋮ On minimum rank and zero forcing sets of a graph ⋮ Failed power domination on graphs ⋮ Critical ideals, minimum rank and zero forcing number ⋮ Odd Cycle Zero Forcing Parameters and the Minimum Rank of Graph Blowups ⋮ Connected zero forcing sets and connected propagation time of graphs ⋮ Matching, path covers, and total forcing sets ⋮ Unnamed Item

Cites Work

• Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns
• Techniques for determining the minimum rank of a small graph
• The minimum rank of symmetric matrices described by a graph: a survey
• Computation of minimal rank and path cover number for certain graphs
• The combinatorial structure of generalized eigenspaces -- from nonnegative matrices to general matrices
• Zero forcing sets and the minimum rank of graphs
• Minimum-rank matrices with prescribed graph
• On the minimum rank of not necessarily symmetric matrices: A preliminary study
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• Graphs whose minimal rank is two

This page was built for publication: Minimum rank problems