Cycle-supermagic labelings of the disjoint union of graphs

Abstract

A graph G(V, E) has an H-covering if every edge in E belongs to a subgraph of G isomorphic to H. Suppose G admits an H-covering. An H-magic labeling is a total labeling A 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 c such that Σ A = Σ_vϵV(A) + Σ_eϵE(A) λ(e) = c. 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 formulate cycle-supermagic labelings for the disjoint union of isomorphic copies of different families of graphs. We also prove that disjoint union of non isomorphic copies of fans and ladders are cycle-supermagic.