Bondage number of the strong product of two trees

Abstract 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 .