Let G= (X,Y,E,) be a bipartite graph. A subset D of X is an X-dominating set if every x € X-D is X-adjacent to at least one vertex  u€ D The cardinality of a minimum X-dominating set is called the X-domination number and is denoted by Y_x (G) . A minimum cardinality subset  S X which dominates all vertices in Y, such a set is called Y-dominating set. The Y-domination number is denoted by Y_y (G) We characterize graphs for which Y_y (G) = Y_y (G) , Y_y (G) = Y_y (G) , Y_hr (G) = I and also prove Y_y (G) ≤ Yx (G)