Group H-magic labelings of graphs

Abstract

A simple graph G admits an H-covering if each edge in E G is a member of a sub- graph of G isomorphic to H. An H-magic labeling of a graph G possessing an H-covering is a bijective function from the vertex-set and the edge-set of the graph G onto the set 1 2 V G E G if there occurs a positive integer , called the magic sum, such that for every subgraph H of G isomorphic to H, the sum wt H v V H v e E H e is equal to . The sum wt H is termed as, the H-weight. A graph is called H-magic (H-supermagic) if it possesses an H-magic (H-supermagic) labeling. If H is isomorphic to K2, then resulting labeling is known as edge-magic total labeling. This dissertation studies about the formulation of cycle-supermagic labelings for the disjoint union of isomorphic and non isomorphic copies of different families of graphs. We also evaluate the K2-supermagic labelings of some families of alpha trees. More- over, we find the cycle-(super)magic labelings of uniform subdivided graph and cycle- supermagic labelings for non uniform subdivisions of fans and triangular ladders graphs. We also articulate about the introduction of H-groupmagic total labeling of a graph G over a finite abelian group A . In this study, we determine the H-groupmagic total labelings of fan graphs and disjoint union of isomorphic as well as non-isomorphic copies of fan graphs over finite abelian group A 3 n, where n 3