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2014 Computing positive semidefinite minimum rank for small graphs
Steven Osborne, Nathan Warnberg
Involve 7(5): 595-609 (2014). DOI: 10.2140/involve.2014.7.595

Abstract

The positive semidefinite minimum rank of a simple graph G is defined to be the smallest possible rank over all positive semidefinite real symmetric matrices whose ij-th entry (for ij) is nonzero whenever {i,j} is an edge in G and is zero otherwise. The computation of this parameter directly is difficult. However, there are a number of known bounding parameters and techniques which can be calculated and performed on a computer. We programmed an implementation of these bounds and techniques in the open-source mathematical software Sage. The program, in conjunction with the orthogonal representation method, establishes the positive semidefinite minimum rank for all graphs of order 7 or less.

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Steven Osborne. Nathan Warnberg. "Computing positive semidefinite minimum rank for small graphs." Involve 7 (5) 595 - 609, 2014. https://doi.org/10.2140/involve.2014.7.595

Information

Received: 19 July 2011; Revised: 13 December 2011; Accepted: 12 December 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1297.05150
MathSciNet: MR3245837
Digital Object Identifier: 10.2140/involve.2014.7.595

Subjects:
Primary: 05C50
Secondary: 15A03

Keywords: graph , matrix , maximum nullity , minimum rank , positive semidefinite , zero forcing , zero forcing number

Rights: Copyright © 2014 Mathematical Sciences Publishers

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