Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix

DOI10.13001/1081-3810.1070zbMath0999.15005OpenAlexW1537990515MaRDI QIDQ2782047

Carlos M. Saiago, Charles R. Johnson

Publication date: 14 April 2002

Published in: The Electronic Journal of Linear Algebra (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/122186

zbMATH Keywords

treealgorithmmultiplicityeigenvaluesymmetric matrixvertex degrees

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Vertex degrees (05C07)

Related Items (13)

The inverse inertia problem for graphs: Cut vertices, trees, and a counterexample ⋮ Computational and Theoretical Challenges for Computing the Minimum Rank of a Graph ⋮ Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns ⋮ The trees for which maximum multiplicity implies the simplicity of other eigenvalues ⋮ The structure of sandpile groups of outerplanar graphs ⋮ 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 multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree ⋮ The structure of matrices with a maximum multiplicity eigenvalue ⋮ Tree decomposition by eigenvectors ⋮ Undirected graphs of Hermitian matrices that admit only two distinct eigenvalues ⋮ 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

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