Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

5-2020

Journal or Book Title

Journal of Combinatorial Theory, Series B

Volume

142

First Page

276

Last Page

306

DOI

10.1016/j.jctb.2019.10.005

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 [Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph. Electron. J. Combin., 2017]. 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.

Comments

This is a manuscript of an article published as Barrett, Wayne, Steve Butler, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Jephian C-H. Lin, Bryan L. Shader, and Michael Young. 142 "The inverse eigenvalue problem of a graph: Multiplicities and minors." Journal of Combinatorial Theory, Series B (2020): 276-306. DOI: 10.1016/j.jctb.2019.10.005. Posted with permission.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Available for download on Sunday, October 31, 2021

Published Version

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