Zero forcing number of Rook’s graphs

A set Z of vertices of a graph G is a zero forcing set of G if all vertices of Z are initially colored black and remaining vertices of G are colored white and then all vertices of G will be turned black after finitely many applications of the color-change rule: If u is the only white neighbor of black vertex v then u is turned black and we say v forces u which is denoted by v ! u. The minimum cardinality of a zero forcing set of graph G is the zero forcing number of G which is denoted by Z(G). Zero forcing and its applications are useful in multiple branches of science like electrical engineering, computational complexity and quantum control. Here we introduce a new presentation of cartesian product of two complete bipartite graphs and compute the zero forcing number of these graphs.