Converse to the Parter--Wiener theorem: the case of non-trees

DOI10.1016/j.disc.2005.04.025zbMath1114.05061OpenAlexW2057096223MaRDI QIDQ856860

Charles R. Johnson, António Leal-Duarte

Publication date: 14 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.disc.2005.04.025

zbMATH Keywords

eigenvalue multiplicitymatrix graph

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 (9)

Graphs with eigenvalue \(-1\) of multiplicity \(2 \theta (G)+ \rho (G) -1\) ⋮ The change in eigenvalue multiplicity associated with perturbation of a diagonal entry ⋮ Geometric Parter-Wiener, etc. theory ⋮ The multiplicity of eigenvalues of unicyclic graphs ⋮ Lower bounds for minimum semidefinite rank from orthogonal removal and chordal supergraphs ⋮ On the minimum semidefinite rank of a simple graph ⋮ Nowhere-zero eigenvectors of graphs ⋮ The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree ⋮ Exact SDP relaxations of quadratically constrained quadratic programs with forest structures

Cites Work

• Unnamed Item
• Spectral multiplicity and splitting results for a class of qualitative matrices
• What are Schur complements, anyway?
• Matrix Analysis
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On the Eigenvalues and Eigenvectors of a Class of Matrices
• Almost principal minors of inverse \(M\)-matrices

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