Graph G contain an H-covering if each edge in G belongs to a subgraph of G isomorphic to H. A graph G is H-magic if there is a total labeling g from each element of graph G to {1,2,...,|V(G)|+|E(G)|}, such that every subgraph H'=(V',E') of G isomorphic to H satisfied g(H')=def∑_(v∈V')g(v)+∑_(e∈E')g(e)=s(g), where s(g) is a magic sum. Furthermore, G contain H-supermagic if label of every vertex is {1,2,...,|V(G)|}. If s(g) form an arithmetic sequence a, a + d, ...,a + (l - 1)d, with a and d are natural numbers, l is the number of, subgraphs of G isomorphic to H we called it antimagic covering. Additionally, if every vertex of G labeled by 1,2 until the order of G, then it is said a super (a, d)-H-antimagic labeling. This research prove that H-supermagic labeling and super (a, d)-H-antimagic labeling on C_n ◇ W_n, with H = P_2 ◇ W_n.
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