All the graphs considered here arefinite and undirected. The terms not defined here are used in the sense of Harary [10]. A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. If the domain of the mapping is the set of vertices (or edges) then the labeling is called a vertex labeling (or an edge labeling). By a (p, q) graph G, we mean a graph G = (V, E) with | V | = p and | E | = q. Graph labeling was first introduced in the late 1960's. Many studies in graph labeling refer to Rosa's research in 1967 [19]. Rosa introduced afunction f from a set of vertices in a graph G to the set of integers {0, 1, 2,..., q}so that each edge xy is assigned the label |f (x) – f (y)|, all labels are distinct. Rosa called this labeling. Independently, Golomb [8] studied the same type of labeling and called as graceful labeling.