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Research Article

Parter vertices and generalization of the downer branch mechanism in the general setting

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Pages 1239-1253 | Received 22 Feb 2022, Accepted 22 Dec 2022, Published online: 19 Feb 2023

References

  • Johnson CR, Leal-Duarte A, Saiago CM. The Parter–Wiener theorem: refinement and generalization. SIAM J Matrix Anal Appl. 2003;25(2):352–361.
  • Johnson CR, Saiago CM. Geometric Parter–Wiener, etc., theory. Linear Algebra Appl. 2018;537:332–347.
  • Johnson CR, Saiago CM, Toyonaga K. The change in multiplicity of an eigenvalue due to adding or removing edges. Linear Algebra Appl. 2019;560:86–99.
  • Johnson CR, Saiago CM, Toyonaga K. Classification of vertices and edges with respect to the geometric multiplicity of an eigenvalue in a matrix, with a given graph, over a field. Linear Multilinear A. 2018;66(11):2168–2182.
  • Johnson CR, Saiago CM. Eigenvalues, multiplicities and graphs, Cambridge tracts in mathematics. Cambridge University Press; 2018.
  • Toyonaga K, Johnson CR. Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue. Linear Multilinear A. 2021;69(10):1803–1812.
  • Johnson CR, Sutton BD. Hermitian matrices, eigenvalue multiplicities, and eigenvector components. SIAM J Matrix Anal Appl. 2004;26(2):390–399.
  • Johnson CR, McMichael PR. The change in multiplicity of an eigenvalue of a Hermitian matrix associated with the removal of an edge from its graph. Discrete Math. 2011;311(2–3):166–170.
  • Johnson CR, Saiago CM, Toyonaga K. Change in vertex status after removal of another vertex in the general setting. Linear Algebra Appl. 2021;612:128–145.

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