NEW NUMBERS ON EULER'S TOTIENT FUNCTION WITH APPLICATIONS.
Shahbaz Ali, Adnan Ali
Abstract
Shahbaz Ali, Adnan Ali
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.}}
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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.}}
Key concepts: Euler's totient function, Mathematics, Mathematical proof, Discrete mathematics, Graph, Combinatorics, Euler's formula, Mathematical analysis