Given graph G, we consider a surjective function r mapping each vertex into a role, a positive integer in {1,2,…,k}. For any two vertices with the same role, if the sets of roles assigned to their neighbors are the same, then we call r a k-role assignment. In this paper we study the k-role assignments under some graph operations including join, cartesian product, lexicographic product, categorical product and Mycielski''s graphs.