Bondage number of strong product of two paths.

The bondage number b( G) of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers m ⩾ 2 and n ⩾ 2, b( P ⊠ P) = 7 − r( m) − r( n) if ( r( m), r( n)) = (1, 1) or (3, 3), 6 − r( m) − r( n) otherwise, where r( t) is a function of positive integer t, defined as r( t) = 1 if t ≡ 1 (mod 3), r( t) = 2 if t ≡ 2 (mod 3), and r( t) = 3 if t ≡ 0 (mod 3). [ABSTRACT FROM AUTHOR]