K-Forcing number for Cartesian product of some graphs

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.