The Bondage Number of Mesh Networks

Abstract

The bondage number $b(G)$ of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with domination number greater than that of $G$. Denote $P_n\times P_m$ be the Cartesian product of two paths $P_n$ and $P_m$. This paper determines that the exact value of $b(P_n\times P_2)$, $b(P_n\times P_3)$ and $b(P_n\times P_4)$ for $n\ge 2$.