The bifurcation lemma for strong properties in the inverse eigenvalue problem of a graph

DOI10.1016/j.laa.2022.04.009zbMath1490.05158arXiv2112.11712OpenAlexW4224272980WikidataQ124799247 ScholiaQ124799247MaRDI QIDQ2144236

H. Tracy Hall, Jephian C.-H. Lin, Shaun M. Fallat, Bryan L. Shader

Publication date: 1 June 2022

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

Full work available at URL: https://arxiv.org/abs/2112.11712

zbMATH Keywords

inverse eigenvalue problemimplicit function theoreminverse function theorembifurcation lemmastrong properties

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) Implicit function theorems; global Newton methods on manifolds (58C15) Sign pattern matrices (15B35)

Related Items (2)

The strong spectral property of graphs: graph operations and barbell partitions ⋮ The allow sequence of distinct eigenvalues for a sign pattern

Cites Work

• Unnamed Item
• The nilpotent-centralizer method for spectrally arbitrary patterns
• Potentially nilpotent patterns and the nilpotent-Jacobian method
• Analysis and algebra on differentiable manifolds: a workbook for students and teachers
• Spectral multiplicity and splitting results for a class of qualitative matrices
• The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample
• Extreme nonnegative matrices
• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• Spectrally arbitrary patterns
• The inverse eigenvalue problem of a graph: multiplicities and minors
• Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph
• The inertia set of a signed graph
• Generating potentially nilpotent full sign patterns
• Nilpotent matrices and spectrally arbitrary sign patterns
• Matrix Analysis
• The Construction of Jacobi and Periodic Jacobi Matrices With Prescribed Spectra
• ON MATRICES DEPENDING ON PARAMETERS
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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