Cm-supermagic labeling of graphs

A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. In this case, we say that G is H-magic if there is a total labeling f:V(G)∪E(G)→{1,2,3,…,|V(G)|+|E(G)|} such that for each subgraph H′ of G isomorphic to H, ∑v∈V(H′)f(v)+∑e∈E(H′)f(e) is constant. When f(V(G))={1,2,3,…,|V(G)|}, we say that G is H-supermagic. In this paper, we generalize some of the results found in the article “A.A.G. Ngurah, A.N.M. Salman, L. Susilowati, H-supermagic labelings of graphs, Discrete Mathematics, 310 (2010), 1293–1300”. Also we provide a partial solution to an open problem found in the same article.