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Article
Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph
The Electronic Journal of Combinatorics
  • Wayne Barrett, Brigham Young University
  • Shaun Fallat, University of Regina
  • H. Tracy Hall, Brigham Young University
  • Leslie Hogben, Iowa State University
  • Jephian C.-H. Lin, Iowa State University
  • Bryan L. Shader, University of Wyoming
Document Type
Article
Publication Version
Published Version
Publication Date
1-1-2017
Abstract

For a given graph G and an associated class of real symmetric matrices whose off- diagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdiere in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities. These new properties are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Finally, these ideas are applied to the minimum number of distinct eigenvalues associated with G, denoted by q(G). The graphs for which q(G) is at least the number of vertices of G less one are characterized.

Comments

This article is published as W. Barrett, S. Fallat, H. T. Hall, L. Hogben, J. C.-H. Lin, B.L. Shader. Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph. Electronic Journal of Combinatorics 24 (2017): P2.40.

Copyright Owner
The Authors
Language
en
File Format
application/pdf
Citation Information
Wayne Barrett, Shaun Fallat, H. Tracy Hall, Leslie Hogben, et al.. "Generalizations of the Strong Arnold Property and the minimum number of distinct eigenvalues of a graph" The Electronic Journal of Combinatorics Vol. 24 Iss. 2 (2017) p. P2.40
Available at: http://0-works.bepress.com.library.simmons.edu/leslie-hogben/86/