Bondage number of grid graphs

TL;DR

This paper investigates the bondage number, which measures the minimum edges removal needed to increase a graph's domination number, specifically focusing on grid-like graphs and their strong and direct product forms.

Contribution

It provides new bounds and exact values for the bondage number of certain grid graphs formed by strong and direct products of paths.

Findings

Bounds and exact values for bondage numbers of grid graphs

Results for strong product of two paths

Results for direct product of two paths

Abstract

The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than the domination number of $G$. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.