Properties of the Zero Forcing Number
Kayla Owens · ScholarsArchive (Brigham Young University) · 2009
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.