“…Bloom and Hsu [2] extended the notion of graceful labeling to directed graphs. Further this work can be extended in the field of automata theory [13,14,15,16,17,18,19] which has a wide range of application in automata theory. There are many applications in graph labeling under undirected [20,24,25,26,27,28,29,30] and directed graph [21,22,23].…”