Cycle-supermagic labelings of the disjoint union of graphs

摘要

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) boolean OR E(G) onto the integers {1, 2, . . . , |V (G) boolean OR E(G)|} with the property that, for every subgraph A of G isomorphic to H there is a positive integer c such that Sigma A = Sigma(v is an element of V(A)) lambda(v) + Sigma(e is an element of E(A)) lambda(e) = c. A graph that admits such a labeling is called H-magic. In addition, if {lambda(v)}(v is an element of V) = {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.