Note on cycle-(super) magic labelings of disconnected graphs

Abstract

An H-magic labeling of a simple graph G is a total labeling λ from V(G) ∪ E(G) onto the integers {1, 2,⋯, |V(G) ∪ E(G)|} with the property that, for every subgraph A of G isomorphic to H there is a positive integer μ such that wtλ(A) = Σ_vϵV(A) λ(v) + Σ_eϵE(A) λ(e) = μ. A graph that admits such a labeling is called H-magic. In addition, if {λ(v)}_vϵv = {1, 2,⋯, |V|}, then the graph is called H-supermagic. In this paper, we solve a problem that, if G is a cycle-(super) magic then disjoint union of G is also cycle-(super) magic. These results are the generalization of results proved in [1] and [11].