Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(G) is called degree coprime G if for every v∈V-D, there exist vertex u∈D such that uv∈E(G) and (deg u,deg v)=1. The minimum cardinality the domination number denoted by γ_cp (G). non-coprime v)≠1. γ_ncp We obtain some graphs.