Vertex Magic Labeling On V_4 for Cartesian product of two cycles

Abstract

Let V4 be an abelian group under multiplication. Let g: E(G) → V4. Then the vertex magic labeling on V4 is induced as g : V(G) → V4 such that g (v) = ∏ g(uv) u where the product is taken over all edges uv of G incident at v is constant. A graph is said to be V4 magic if it admits a vertex magic labeling on V4. In this paper, we prove that Cm × Cn,m ≥ 3, n ≥ 3, Generalized fish graph, Double cone graph and four Leaf Clover graph are all V4 -magic graphs. Keyword: Vertex magic labeling on V4, V4 -magic graph, Four Leaf Clover Graph. AMS subject classification (2010): 05C78