Campus Units
Mathematics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
2017
Journal or Book Title
arXiv
Abstract
The inverse eigenvalue problem of a given graph G is to determine all possible spectra of real symmetric matrices whose off-diagonal entries are governed by the adjacencies in G. Barrett et al. introduced the Strong Spectral Property (SSP) and the Strong Multiplicity Property (SMP) in [8]. In that paper it was shown that if a graph has a matrix with the SSP (or the SMP) then a supergraph has a matrix with the same spectrum (or ordered multiplicity list) augmented with simple eigenvalues if necessary, that is, subgraph monotonicity. In this paper we extend this to a form of minor monotonicity, with restrictions on where the new eigenvalues appear. These ideas are applied to solve the inverse eigenvalue problem for all graphs of order five, and to characterize forbidden minors of graphs having at most one multiple eigenvalue.
Copyright Owner
The Authors
Copyright Date
2017
Language
en
File Format
application/pdf
Recommended Citation
Barrett, Wayne; Butler, Steve; Fallat, Shaun M.; Hall, H. Tracy; Hogben, Leslie; Lin, Jephian C.-H.; Shader, Bryan L.; and Young, Michael, "The inverse eigenvalue problem of a graph: Multiplicities and minors" (2017). Mathematics Publications. 199.
https://lib.dr.iastate.edu/math_pubs/199
Comments
This is a pre-print of the article Barrett, Wayne, Steve Butler, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Bryan L. Shader, and Michael Young. "The inverse eigenvalue problem of a graph: Multiplicities and minors." arXiv preprint arXiv:1708.00064v1 (2017). Posted with permission.