A graph G=(V,E) with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each of adjacent vertices are relatively prime. A graph G which admits prime labeling is called prime graph. In the present work we investigate some cases of graph which admit prime labeling. We also introduce the concept of union of prime labeling and investigate some results concern to it. Some interesting techniques to determine prime labeling of either union Cnk or union of cycle, c2kUc2mUcn, c2kUc2kUc2n+1 and c2kUc2kUc2mUcn, crown graphs,helm graphs,book graphs and ck(cn) graph and that some families are prime labeling.