  Zero forcing is a process that models the spread of information throughout a
graph as white vertices are forced to turn blue using a color change rule. The
idea of throttling, introduced in 2013 by Butler and Young, is to optimize the
trade-off between the number of initial blue vertices and the time taken to
force all vertices to become blue. The original throttling number of a graph
minimizes the sum of these two quantities and the product throttling number
minimizes their product. In addition, weighted throttling changes the weights
given to these two quantities when minimizing their sum. Since its
introduction, throttling has expanded to include many variants of zero forcing.
This motivates the study of zero forcing and throttling using abstract color
change rules. Recently, it has been shown that the graphs with high (sum)
throttling numbers are characterized by a finite family of forbidden induced
subgraphs. In this paper, we extend that result to throttling, product
throttling, and weighted throttling using abstract color change rules. To this
end, we define some important families of color change rules and explore their
properties.
