For every positive integer k, a simple graph G of order p and size q is said to be k-prime total labeling if there exists a one-one and onto function g whose vertex and edge labels are from k to k+p+q-1 such that for any edge uv inE(G); g(u), g(v), g(uv) are comparatively prime in pairs. Such a graph is known as the k-prime total graph. In our present study, we analyze some class of union of graphs that admit k-prime total labeling for each positive integer k. …