  Zero forcing is a combinatorial game played on graphs that can be used to
model the spread of information with repeated applications of a color change
rule. In general, a zero forcing parameter is the minimum number of initial
blue vertices that are needed to eventually color every vertex blue with a
given color change rule. Furthermore, the throttling number minimizes the sum
of the number of initial blue vertices and the time taken for all vertices to
become blue. In 2013, Barioli et al. added a new rule, called hopping, to
existing color change rules in order to demonstrate that the minor monotone
floor of various zero forcing parameters is itself, a zero forcing parameter.
In this paper, we examine the hopping color change rule independently from the
other classic rules. Specifically, we study the hopping forcing number and the
hopping throttling number. We investigate the ways in which these numbers are
related to various graph theory parameters (such as vertex connectivity and
independence number) as well as other zero forcing parameters.
