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

Positive Semidefinite Initial Cost Product Throttling