The inertia set of the join of graphs

DOI10.1016/j.laa.2010.12.022zbMath1227.05178OpenAlexW2163088586MaRDI QIDQ632470

H. Tracy Hall, Hein van der Holst, Wayne W. Barrett

Publication date: 25 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.12.022

zbMATH Keywords

inertiasymmetric matricesminimum rank problemjoin of graphscombinatorial matrix theory

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (5)

The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph ⋮ Corrigendum to: ``Achievable multiplicity partitions in the inverse eigenvalue problem of a graph ⋮ Unnamed Item ⋮ Graphs that allow all the eigenvalue multiplicities to be even ⋮ Achievable multiplicity partitions in the inverse eigenvalue problem of a graph

Cites Work

• Unnamed Item
• Linearly independent vertices and minimum semidefinite rank
• The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample
• On the minimum rank of the join of graphs and decomposable graphs
• The minimum rank of symmetric matrices described by a graph: a survey
• Inertia sets for graphs on six or fewer vertices
• Graphs whose minimal rank is two

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