Zk-Magic Labeling of Some Families of Graphs

For any non-trivial abelian group A under addition a graph G is said to be A-magic if there exists a labeling f : E(G) → A − {0} such that, the vertex labeling f+ defined as f+(v) = P f(uv) taken over all edges uv incident at v is a constant. An A-magic graph G is said to be Zk-magic graph if the group A is Zk the group of integers modulo k. These Zk-magic graphs are referred to as k-magic graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, G ⊙ Km, m-splitting graph of a path and m-shadow graph of a path are Zk-magic graphs.