Graph labeling is an active area of research in graph theory which has mainly evolved through its many applications in coding theory, communication networks, mobile telecommunication system. Optimal circuits layouts or graph decompositions problems, no name just a few of them.
Most graph labeling methods trace their origion to one introduced by Rosa [1] called such a labeling a β-valuation and Golomb [2] subsequently called graceful labeling, and one introduced by Graham and Sloane [3] called harmonious labeling. Several infinite families of graceful and harmonious graphs have been reported. Many illustrious works on graceful graphs brought a tide to different ways of labeling the elements of graph such as odd graceful