Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

6-2014

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

27

First Page

444

Last Page

457

DOI

10.13001/1081-3810.1629

Abstract

Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530-563, 2009.], whether the maximum nullity is equal to the zero forcing number for all complete subdivision graphs. We prove that this equality holds. Furthermore, we compute the value of M(F,(G) = Z(G) by introducing the bridge tree of a connected graph. Since this equality is valid for all fields, G has field independent minimum rank, and we also show that G has a universally optimal matrix.

Comments

This article is published as Barrett, Wayne, Steve Butler, Minerva Catral, Shaun Fallat, H. Hall, Leslie Hogben, and Michael Young. "The maximum nullity of a complete subdivision graph is equal to its zero forcing number." The Electronic Journal of Linear Algebra 27 (2014): 444-457. DOI: 10.13001/1081-3810.1629. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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