Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

6-2008

Journal or Book Title

Linear Algebra and its Applications

Volume

426

DOI

10.1016/j.laa.2007.12.004

Abstract

Orthogonal representations are used to show that complements of certain sparse graphs have (positive semidefinite) minimum rank at most 4. This bound applies to the complement of a 2-tree and to the complement of a unicyclic graph. Hence for such graphs, the sum of the minimum rank of the graph and the minimum rank of its complement is at most two more than the order of the graph. The minimum rank of the complement of a 2-tree is determined exactly.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 428 (2008); 2560, doi:10.1016/j.laa.2007.12.004. 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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