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2015 Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs
Adam Berliner, Nathan Warnberg, Michael Young, Cora Brown, Joshua Carlson, Nathanael Cox, Leslie Hogben, Jason Hu, Katrina Jacobs, Kathryn Manternach, Travis Peters
Involve 8(1): 147-167 (2015). DOI: 10.2140/involve.2015.8.147

Abstract

An oriented graph is a simple digraph obtained from a simple graph by choosing exactly one of the two arcs (u,v) or (v,u) to replace each edge {u,v}. A simple digraph describes the zero-nonzero pattern of off-diagonal entries of a family of (not necessarily symmetric) matrices. The 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 and path cover number are related parameters. We establish bounds on the range of possible values of all these parameters for oriented graphs, establish connections between the values of these parameters for a simple graph G, for various orientations G and for the doubly directed digraph of G, and establish an upper bound on the number of arcs in a simple digraph in terms of the zero forcing number.

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Adam Berliner. Nathan Warnberg. Michael Young. Cora Brown. Joshua Carlson. Nathanael Cox. Leslie Hogben. Jason Hu. Katrina Jacobs. Kathryn Manternach. Travis Peters. "Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs." Involve 8 (1) 147 - 167, 2015. https://doi.org/10.2140/involve.2015.8.147

Information

Received: 31 December 2013; Accepted: 30 April 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1309.05115
MathSciNet: MR3321717
Digital Object Identifier: 10.2140/involve.2015.8.147

Subjects:
Primary: 05C20‎ , 05C50 , 15A03

Keywords: maximum nullity , minimum rank , oriented graph , path cover number , simple digraph , zero forcing number

Rights: Copyright © 2015 Mathematical Sciences Publishers

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