The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph

DOI10.1016/j.disc.2010.10.010zbMath1225.05168OpenAlexW2064321059MaRDI QIDQ615995

Paul R. McMichael, Charles R. Johnson

Publication date: 7 January 2011

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

Full work available at URL: https://scholarworks.wm.edu/cgi/viewcontent.cgi?article=2475&context=aspubs

zbMATH Keywords

treeHermitian matrixeigenvalue multiplicitymatrix with a given 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

The change in multiplicity of an eigenvalue due to adding or removing edges, The effect of removing a 2-downer edge or a cut 2-downer edge triangle for an eigenvalue, The effect of perturbation of an off-diagonal entry pair on the geometric multiplicity of an eigenvalue, The classification of edges and the change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the change in an edge value, The change in multiplicity of an eigenvalue of a real symmetric matrix resulting from the changes in edge values around a classified vertex in a tree, Classification of vertices and edges with respect to the geometric multiplicity of an eigenvalue in a matrix, with a given graph, over a field, Normalized Laplacian eigenvalues with chromatic number and independence number of graphs, Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue, The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

Cites Work

• The Parter--Wiener Theorem: Refinement and Generalization
• Hermitian Matrices, Eigenvalue Multiplicities, and Eigenvector Components