NEW NUMBERS ON EULER'S TOTIENT FUNCTION WITH APPLICATIONS.

Abstract

For any positive integer $m, ~\varphi(m)$ find out how many residues of $m$ thats are co-prime to $m$, where $\varphi$ is theEuler's totient function. In this work, we introduce the notion oftotient, super totient and hyper totient numbers and discuss their relations.  Many postulates and characterizations of these numbers have been proposed with straight forward   proofs. Finally, applications of these    numbers in graph labeling have been demonstrated over a family of well known graph.}}