Ordered multiplicity lists for eigenvalues of symmetric matrices whose graph is a linear tree

DOI10.1016/j.disc.2014.04.030zbMath1298.05068OpenAlexW2171302729MaRDI QIDQ400401

Andrew A. Li, Andrew J. Walker, Charles R. Johnson

Publication date: 21 August 2014

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2014.04.030

zbMATH Keywords

multiplicityeigenvaluesymmetric matrixlinear tree

Mathematics Subject Classification ID

Trees (05C05) Vertex degrees (05C07)

Related Items (11)

The change in multiplicity of an eigenvalue due to adding or removing edges ⋮ Questions, conjectures, and data about multiplicity lists for trees ⋮ Multiplicities: Adding a Vertex to a Graph ⋮ Multiplicity lists for symmetric matrices whose graphs have few missing edges ⋮ The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a 2-linear tree ⋮ The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a linear tree ⋮ Diameter minimal trees ⋮ Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments ⋮ The inverse eigenvalue problem for linear trees ⋮ The minimum number of multiplicity 1 eigenvalues among real symmetric matrices whose graph is a nonlinear tree ⋮ The proportion of trees that are linear

Cites Work

• Spectral multiplicity and splitting results for a class of qualitative matrices
• On acyclic and unicyclic graphs whose minimum rank equals the diameter
• Eigenvalue assignments and the two largest multiplicities in a Hermitian matrix whose graph is a tree
• 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.
• On the possible multiplicities of the eigenvalues of a Hermitian matrix whose graph is a tree
• On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
• The implicit construction of multiplicity lists for classes of trees and verification of some conjectures
• Structured inverse eigenvalue problems
• Implicit construction of multiple eigenvalues for trees
• Matrix Analysis
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices
• On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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