 On the rook's graph a -dominating set is a set of vertices whose corresponding squares attack all other squares (via a rook's move) at least times.A -tuple dominating set on the rook's graph is a set of vertices whose corresponding squares attack all other squares at least times and are themselves attacked at least times.The minimum cardinality among all -dominating and -tuple dominating sets are the -domination number and the -tuple domination number, respectively.