PATH UNION OF n NON ISOMORPHIC COPIES OF COMPLETE BIPARTITE GRAPH IS ODD GRACEFUL

In 1991, Gnanajothi [4] introduced a labeling method called odd graceful labeling to label the vertices of a graph. A graph G with q edges is said to be odd
graceful if there is an injection f from V (G) → {0,1,2,3,...,(2q-1)} such that, when each edge xy is assigned the label |f(x) - f(y)|, the resulting edge labels are 1,3,5,...,(2q-1). In this paper, we prove that path union of n non isomorphic copies of complete bipartite graph is odd graceful, when m is even.