Bondage number of the strong product of two trees.

The bondage number b(G) of a nonempty graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with domination number greater than that of G. It is known that b(T)≤2 for any nontrivial tree T. In this paper, we obtain that the bondage number of the strong product of two nontrivial trees b(T⊠T′) is equal to b(T)b(T′) or b(T)b(T′)+1, which implies that b(T⊠T′) is equal to 1, 2, 3, 4 or 5.