V-Super and E-Super Vertex-Magic Total Labeling of Graphs

Let G be a graph of order p and size q. A vertex-magic total labeling is an assignment of the integers 1, 2, . . . , p + q to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic constant of G. Such a labeling is V-super vertex-magic total if f(V(G) = {1, 2, . . . , p}, and is an E-super vertex-magic total if f(E(G) = {1, 2, . . . , q}. A graph that admits a V-super vertex-magic total labeling is called V-super vertex-magic total. Similarly, a graph that admits an E-super vertex-magic total labeling is called E-super vertex-magic total. In this paper, we provide some properties of E-super vertex-magic total labeling of graphs and we prove V-super and E-super vertex-magic total labeling of the product of cycles Cm x Cn, where m, n ≥3 and m, n odd.