Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

5-2007

Journal or Book Title

Linear Algebra and its Applications

Volume

423

DOI

10.1016/j.laa.2006.08.003

Abstract

For a given simple graph G, S(G) is defined to be the set of real symmetric matrices A whose (i,j)th entry is nonzero whenever i≠j and ij is an edge in G. In [F. Barioli, S. Fallat, L. Hogben, A variant on the graph parameters of Colin de Verdière: Implications to the minimum rank of graphs, Electron. J. Linear Algebra 13 (2005) 387–404.], ξ(G) is defined to be the maximum corank (i.e., nullity) among A∈S(G) having the Strong Arnold Property; ξ is used to study the minimum rank/maximum eigenvalue multiplicity problem for G. Since ξ is minor monotone, the graphs G such that ξ(G)⩽k can be described by a finite set of forbidden minors. We determine the forbidden minors for ξ(G)⩽2 and present an application of this characterization to computation of minimum rank among matrices in S(G).

Comments

This is a manuscript of an article from Linear Algebra and its Applications 423 (2007): 42, doi:10.1016/j.laa.2006.08.003. Posted with permission.

Rights

This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Owner

Elsevier Inc.

Language

en

File Format

application/pdf

Published Version

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