On the double bondage number of graphs products

Abstract

A set $D$ of vertices of graph $G$ is called $double$ $dominating$ $set$ if for any vertex $v$, $|N[v]cap D|geq 2$. The minimum cardinality of $double$ $domination$ of $G$ is denoted by $gamma_d(G)$. The minimum number of edges $E'$ such that $gamma_d(Gsetminus E)>gamma_d(G)$ is called the double bondage number of $G$ and is denoted by $b_d(G)$. This paper determines that $b_d(Gvee H)$ and exact values of $b(P_ntimes P_2)$, and generalized corona product of graphs.