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.
Copyright Owner
The Author(s)
Copyright Date
2009
Language
en
File Format
application/pdf
Recommended Citation
DeAlba, Luz M.; Grout, Jason; Hogben, Leslie; Mikkelson, Rana; and Rasmussen, Kaela, "Universally optimal matrices and field independence of the minimum rank of a graph" (2009). Mathematics Publications. 244.
https://lib.dr.iastate.edu/math_pubs/244
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.