Let G be a connected graph. For M⊆V(G), for each v ϵ V(G) the monophonic resolving set is mr "(" v/M") = " (d_m (v,v_1 ),d_m (v,v_2 )…d_m (v,v_k )), where M={v_1,v_2….v_k}. M is said to be a monophonic resolving set of G, if mr(v/M)≠mr(u/M) for every u,v∈V(G), where u≠v. The minimum cardinality of a monophonic resolving set is called the monophonic dimension of G. It is denoted by mdim(G). A set M⊆V(G) is said to be a monophonic resolving dominating set of G. If G is both a monophonic resolving set and a dominating set of G.The minimum cardinality of a monophonic resolving dominating set of G is the monophonic resolving domination number of G and is denoted by γ_mdim (G). Any monophonic resolving set of cardinality γ_mdim (G) is called a γ_mdim- set of G. In this article, the monophonic domination dimension number of some standard graphs are determined.