  Product throttling answers the question of minimizing the product of the
resources needed to accomplish a task, and the time in which it takes to
accomplish the task. In product throttling for positive semidefinite zero
forcing, task that we wish to accomplish is positive semidefinite zero forcing.
Positive semidefinite zero forcing is a game played on a graph $G$ that starts
with a coloring of the vertices as white and blue. At each step any vertex
colored blue with a unique white neighbor in a component of the graph formed by
deleting the blue vertices from $G$ forces the color of the white neighbor to
become blue. We give various results and bounds on the initial cost product
throttling number, including a lower bound of $1+rad(G)$ and the initial cost
product throttling number of a cycle. We also include a table with results on
the initial cost and no initial cost product throttling number for various
graph families.
