The zero blocking numbers of grid graphs

Abstract

In a zero forcing process, vertices of a graph are colored black and white initially, and if there exists a black vertex adjacent to exactly one white vertex, then the white vertex is forced to be black. A zero blocking set is an initial set of white vertices in a zero forcing process such that ultimately there exists a white vertex. The zero blocking number is the minimum size of a zero blocking set. This paper gives the exact value of the zero blocking number of grid graphs.