Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

7-2009

Journal or Book Title

Electronic Journal of Linear Algebra

Volume

18

First Page

403

Last Page

419

DOI

10.13001/1081-3810.1321

Abstract

The minimum rank of a simple graph G over a field F is the smallest possible rank among all symmetric matrices over F whose (i, j)th entry ( for i not equal j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A universally optimal matrix is defined to be an integer matrix A such that every off-diagonal entry of A is 0, 1, or -1, and for all fields F, the rank of A is the minimum rank over F of its graph. Universally optimal matrices are used to establish field independence of minimum rank for numerous graphs. Examples are also provided verifying lack of field independence for other graphs.

Comments

This article is published as DeAlba, Luz, Jason Grout, Leslie Hogben, Rana Mikkelson, and Kaela Rasmussen. "Universally optimal matrices and field independence of the minimum rank of a graph." The Electronic Journal of Linear Algebra 18 (2009): 403-419. DOI: 10.13001/1081-3810.1321. Posted with permission.

Copyright Owner

The Author(s)

Language

en

File Format

application/pdf

Included in

Algebra Commons

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