New Classes of Odd Graceful Graphs

In this paper, we introduce the notions of m-shadow graphs and n-splitting graphs,m ≥ 2, n ≥ 1. We prove that, the m-shadow graphs for paths, complete bipartite graphs and symmetric product between paths and null graphs are odd graceful. In addition, we show that, the m-splitting graphs for paths, stars and symmetric product between paths and null graphs are odd graceful. Finally, we present some examples to illustrate the proposed theories.