On group vertex magic graphs

Abstract

Let be a simple undirected graph and let be an additive abelian group with identity 0. A mapping is said to be a -vertex magic labeling of if there exists an element of such that for any vertex of , where is the open neighborhood of A graph that admits such a labeling is called an -vertex magic graph. If is -vertex magic graph for any nontrivial abelian group , then is called a group vertex magic graph. In this paper, we obtain a few necessary conditions for a graph to be group vertex magic. Further, when , we give a characterization of trees with diameter at most 4 which are -vertex magic.

Keywords

• -vertex magic
• group vertex magic graph
• weight of a vertex
• tree