New Numbers on Euler's Totient Function with Applications

For any positive integer m, phi(m) finds out how many residues of m that are co-prime to m, where phi is the Euler's totient function. In this paper, we introduce the notion of totient and hyper totient numbers. We explore the potential links of totient, super totient and hyper totient numbers. Many postulates and characterizations of these numbers have been proposed with straight forward proofs. In the end, applications of these numbers in graph labeling have also been demonstrated over a family of well known graph.