Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs

Thumbnail Image
Date
2015-01-01
Authors
Berliner, Adam
Brown, Cora
Carlson, Joshua
Cox, Nathanael
Hogben, Leslie
Hu, Jason
Jacobs, Katrina
Manternach, Kathryn
Peters, Travis
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
Organizational Unit
Journal Issue
Is Version Of
Versions
Series
Department
Mathematics
Abstract

An oriented graph is a simple digraph obtained from a simple graph by choosing exactly one of the two arcs (u,v)(u,v) or (v,u)(v,u) to replace each edge {u,v}{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 GG, for various orientations G→G→ and for the doubly directed digraph of GG, and establish an upper bound on the number of arcs in a simple digraph in terms of the zero forcing number.

Comments

This is an article from Involve 8 (2015): 147, doi:10.2140/involve.2015.8.147. Posted with permission.

Description
Keywords
Citation
DOI
Copyright
Thu Jan 01 00:00:00 UTC 2015
Collections