Supermagic coverings of the disjoint union of graphs and amalgamations

Let H be a graph. A graph G = ( V , E ) admits an H -covering if every edge in E belongs to a subgraph of G isomorphic to H . A graph G is called H -magic if there is a fixed integer k and a total labeling f : V ∪ E → { 1 , 2 , … , | V | + | E | } such that for each subgraph H ′ = ( V ′ , E ′ ) of G isomorphic to H , ∑ v ∈ V ′ f ( v ) + ∑ e ∈ E ′ f ( e ) = k . If f ( V ) = { 1 , 2 , … , | V | } , then G is H -supermagic. In this paper, we investigate the G -supermagicness of a disjoint union of c copies of a graph G . We characterize all such graphs of being G -supermagic. We also show that a disjoint union of any paths is c P h -supermagic for some c and h . Besides, we prove that certain subgraph-amalgamation of graphs G is G -supermagic.