On H-supermagic labelings for certain shackles and amalgamations of a connected graph

Abstract

Let H be a graph. A graph G= (V, E) is said to be H-magic if every edge of G belongs to at least one subgraph isomorphic to H and there is a total labeling f : V ∪ E → {1,2,..., |V| + |E|} such that for each subgraph H′ = (V′, E′) of G isomorphic to H, the sum of all vertex labels in V plus the sum of all edge labels in E′ is a fixed constant. Additionally, G is said to be H-supermagic if f(V) = {1,2.....|V|}. We study H-supermagic labelings of some graphs obtained from k isomorphic copies of a connected graph H. By using a k-balanced partition of multisets, we prove that certain shackles and amalgamations of a connected graph H are H-supermagic.