The zero blocking numbers of grid graphs

TL;DR

This paper determines the exact zero blocking number for grid graphs, providing insights into the minimal initial white vertices needed to eventually leave some vertices white in a zero forcing process.

Contribution

It presents the exact zero blocking number for grid graphs, a novel result in the study of zero forcing parameters.

Findings

Exact zero blocking number for grid graphs derived

Provides a formula for the zero blocking number in grid graphs

Enhances understanding of zero forcing dynamics in grid structures

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.