A simple graph G = (V, E) admits a H-covering, where H is subgraph of G, if every edge in E belongs to a subgraph of G isomorphic to H. Graph G is H-magic if there is a total labeling f:V(G) ∪ E(G) → 1, 2, ..., |V(G)| + |E(G)|, such that each subgraph H' = (V',E') of G isomorphic to H and satisfying f(H')_=~(def) ∑_(v∈V')f(v) + ∑_(e∈E')f(e) = m(f) where m(f) is a constant magic sum. Additionaly, G admits H-supermagic if f(V) = 1, 2, ..., |V|. The edge corona C_n ◇ P_n of C_n and P_n is defined as the graph obtained by taking one copy of C_n and n copies of P_n, and then joining two end-vertices of the i-th edge of C_n to every vertex in the i-th copy of P_n. This research aim is to find H-supermagic covering on an edge corona product of cycle and path graph C_n ◇ P_n where H is P_2 ◇ P_n. We use k-balanced multiset to solve our reserarch. Here, we find that an edge corona product of cycle and path graph C_n ◇ P_n is P_2 ◇ P_n supermagic for n > 3.
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机译：一个简单的图形g =（v，e）承认h覆盖物，其中h是g的子图，如果e中的每个边缘属于g同胞对h的子图。图g是h-marg，如果存在总标签F：v（g）∪e（g）→1,2，...，| v（g）| + | e（g）|，使得g同构至h的每个子图H'=（v'，e'）并且满足f（h'）_ =〜（def）σ_（v∈v'）f（ v）+σ_（e∈e'）f（e）= m（f）其中m（f）是恒定的魔法。辅助，G承认H-Supermagic如果f（v）= 1,2，...，| v |。 C_N和P_N的边缘电晕C_N◇P_N定义为通过拍摄P_N的一个副本，然后将C_N的第二个边缘的第二个顶点连接到I-中的每个顶点所获得的图p_n的副本。该研究目的是在循环和路径图C_N◇P_N为P_2◇P_N的P_N◇P_N的边缘电晕产品上找到H-Supermagic覆盖物。我们使用K-Bandancd Multiset来解决我们的重立阵列。在这里，我们发现循环和路径图C_N◇P_N的边缘电晕产物是P_2◇P_N Supermagic for N> 3。
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