Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2017

Journal or Book Title

The Electronic Journal of Combinatorics

Volume

24

Issue

2

First Page

P2.40

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

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