The liberation set in the inverse eigenvalue problem of a graph

DOI10.1016/j.laa.2023.06.009arXiv2302.01670OpenAlexW4381188774MaRDI QIDQ6168543

Polona Oblak, Helena Šmigoc, Jephian C.-H. Lin

Publication date: 9 August 2023

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

Full work available at URL: https://arxiv.org/abs/2302.01670

zbMATH Keywords

inverse eigenvalue problemsymmetric matrixzero forcingstrong spectral propertymatrix liberation lemma

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) Numerical solutions to inverse eigenvalue problems (65F18)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The nowhere-zero eigenbasis problem for a graph
• Using a new zero forcing process to guarantee the strong Arnold property
• The maximum of the minimal multiplicity of eigenvalues of symmetric matrices whose pattern is constrained by a graph
• Construction of matrices with a given graph and prescribed interlaced spectral data
• Inverse eigenvalue problems for Jacobi matrices
• Construction of a Jacobi matrix from spectral data
• Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: The case of generalized stars and double generalized stars.
• Sur un nouvel invariant des graphes et un critère de planarité. (On a new graph invariant and a planarity criterion)
• On the construction of a Jacobi matrix from spectral data
• The inverse eigenvalue problem of a graph: multiplicities and minors
• The inverse eigenvalue problem for linear trees
• The strong spectral property for graphs
• On the inverse eigenvalue problem for block graphs
• Generalizations of the strong Arnold property and the minimum number of distinct eigenvalues of a graph
• Zero forcing sets and the minimum rank of graphs
• The Construction of Jacobi and Periodic Jacobi Matrices With Prescribed Spectra
• Ordered multiplicity inverse eigenvalue problem for graphs on six vertices
• Inverse Problems and Zero Forcing for Graphs
• A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs

This page was built for publication: The liberation set in the inverse eigenvalue problem of a graph