Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

8-2010

Journal or Book Title

Linear Algebra and its Applications

Volume

433

First Page

401

Last Page

411

DOI

10.1016/j.laa.2010.03.008

Abstract

The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity/minimum rank of the family of symmetric matrices described by G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive semidefinite zero forcing number Z+(G) is introduced, and shown to be equal to |G|-OS(G), where OS(G) is the recently defined ordered set number that is a lower bound for minimum positive semidefinite rank. The positive semidefinite zero forcing number is applied to the computation of positive semidefinite minimum rank of certain graphs. An example of a graph for which the real positive symmetric semidefinite minimum rank is greater than the complex Hermitian positive semidefinite minimum rank is presented.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 433 (2010): 401, doi:10.1016/j.laa.2010.03.008. Posted with permission.

Rights

This manuscript version is made available under the CC-BY-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

Included in

Algebra Commons

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