#### Abstract

The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, including its behavior under various graph operations.

#### Degree

MS

#### College and Department

Physical and Mathematical Sciences; Mathematics

#### Rights

http://lib.byu.edu/about/copyright/

#### BYU ScholarsArchive Citation

Owens, Kayla Denise, "Properties of the Zero Forcing Number" (2009). *All Theses and Dissertations*. 2216.

http://scholarsarchive.byu.edu/etd/2216

#### Date Submitted

2009-07-06

#### Document Type

Thesis

#### Handle

http://hdl.lib.byu.edu/1877/etd2999

#### Keywords

Graph Theory, Zero Forcing, Minimum rank, symmetric matrix, maximum nullity