Abstract
$k$-Forcing is an iterative graph coloring process based on a color change rule that describes how to color the vertices. $k$-Forcing is a generalization of zero forcing that is useful in multiple scientific branches, such as quantum control. In this paper, we investigate the $k$-forcing number of the Cartesian product of some graphs. The main contribution of this paper is to determine the $k$-forcing number of the Cartesian product of two complete bipartite graphs using a new representation of this graph.
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