Campus Units

Mathematics

Document Type

Article

Publication Version

Published Version

Publication Date

2015

Journal or Book Title

Involve

Volume

8

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)(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.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

Share

COinS