Bondage number of grid graphs
Magda Dettlaff, Magdalena Lemanska, Ismael G. Yero

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 of a nonempty graph is the cardinality of a smallest set of edges whose removal from results in a graph with domination number greater than the domination number of . 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.
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