Minimum rank, maximum nullity, and zero forcing number of simple digraphs

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2013-11-01
Authors
Berliner, Adam
Catral, Minerva
Hogben, Leslie
Hogben, Leslie
Huynh, My
Lied, Kelsey
Young, Michael
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Mathematics
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Electrical and Computer EngineeringMathematics
Abstract

A simple digraph describes the off-diagonal zero-nonzero pattern of a family of (not necessarily symmetric) matrices. Minimum rank of a simple digraph is the minimum rank of this family of matrices; maximum nullity is defined analogously. The simple digraph zero forcing number is an upper bound for maximum nullity. Cut-vertex reduction formulas for minimum rank and zero forcing number for simple digraphs are established. The effect of deletion of a vertex on minimum rank or zero forcing number is analyzed, and simple digraphs having very low or very high zero forcing number are characterized.

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This article is published as Berliner, Adam, Minerva Catral, Leslie Hogben, My Huynh, Kelsey Lied, and Michael Young. "Minimum rank, maximum nullity, and zero forcing number of simple digraphs." The Electronic Journal of Linear Algebra 26 (2013): 762-780. DOI: 10.13001/1081-3810.1686. Posted with permission.

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