Campus Units
Mathematics
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
6-2010
Journal or Book Title
Linear Algebra and its Applications
Volume
432
DOI
10.1016/j.laa.2010.01.008
Abstract
The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. Minimum rank is a difficult parameter to compute. However, there are now a number of known reduction techniques and bounds that can be programmed on a computer; we have developed a program using the open-source mathematics software Sage to implement several techniques. We have also established several additional strategies for computation of minimum rank. These techniques have been used to determine the minimum ranks of all graphs of order 7.
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.
Copyright Date
2010
Language
en
File Format
application/pdf
Recommended Citation
DeLoss, Laura; Grout, Jason; Hogben, Leslie; McKay, Tracy; Smith, Jason; and Tims, Geoff, "Techniques for determining the minimum rank of a small graph" (2010). Mathematics Publications. 64.
https://lib.dr.iastate.edu/math_pubs/64
Comments
This is a manuscript of an article from Linear Algebra and its Applications 432 (2010): 2995, doi:10.1016/j.laa.2010.01.008. Posted with permission.