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.

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.

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.

Language

en

File Format

application/pdf

Published Version

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