On the minimum rank of the join of graphs and decomposable graphs

DOI10.1016/j.laa.2006.05.020zbMath1112.05061OpenAlexW2006666423MaRDI QIDQ869896

Francesco Barioli, Shaun M. Fallat

Publication date: 9 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2006.05.020

zbMATH Keywords

cographsmaximum multiplicityinertia-balanced

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 (16)

Linearly independent vertices and minimum semidefinite 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 ⋮ Bordering of symmetric matrices and an application to the minimum number of distinct eigenvalues for the join of graphs ⋮ On the graph complement conjecture for minimum rank ⋮ Computing inertia sets using atoms ⋮ The inertia set of the join of graphs ⋮ The minimum rank of matrices and the equivalence class graph ⋮ On the minimum semidefinite rank of a simple graph ⋮ On acyclic and unicyclic graphs whose minimum rank equals the diameter ⋮ Minimum rank of skew-symmetric matrices described by a graph ⋮ The Colin de Verdière number and joins of graphs ⋮ Critical ideals, minimum rank and zero forcing number ⋮ The minimum rank of symmetric matrices described by a graph: a survey ⋮ The maximum multiplicity of the largest \(k\)-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Cites Work

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• Laplacian graph eigenvectors
• The rank of a cograph
• On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
• Computation of minimal rank and path cover number for certain graphs
• Laplacian spectra and spanning trees of threshold graphs
• A characterization of tridiagonal matrices
• On the difference between the maximum multiplicity and path cover number for tree-like graphs
• Matrix Analysis
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• Graphs whose minimal rank is two
• Graphs whose minimal rank is two: The finite fields case

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