Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

10-2008

Journal or Book Title

Linear Algebra and its Applications

Volume

429

DOI

10.1016/j.laa.2008.04.038

Abstract

For a graph G of order n, the minimum rank of G is defined to be the smallest possible rank over all real symmetric n×n matrices A whose (i,j)th entry (for i≠j) is nonzero whenever {i,j} is an edge in G and is zero otherwise. We prove an upper bound for minimum rank in terms of minimum degree of a vertex is valid for many graphs, including all bipartite graphs, and conjecture this bound is true over for all graphs, and prove a related bound for all zero-nonzero patterns of (not necessarily symmetric) matrices. Most of the results are valid for matrices over any infinite field, but need not be true for matrices over finite fields.

Comments

This is a manuscript of an article from Linear Algebra and its Applications 429 (2008): 1629, doi: 10.1016/j.laa.2008.04.038. 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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