Novel classes of integers and their applications in graph labeling

Authors : Shahbaz ALİ, Muhammad Khalid MAHMOOD, K P SHUM

Pages : 1094-1110

Doi:10.15672/hujms.825723

View : 17 | Download : 9

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :Adding new classes of integers to literature is both challenging and charming. Until a new class is completely characterized, mathematics is never going to be worth it. While it`s absurd to play with integers without intended consequences. In this work, we introduce and investigate four new classes of integers namely, anti-totient numbers, half anti-totient numbers, near Zumkeller numbers and half near Zumkeller numbers by using the notion of non-coprime residues of $n$ including $n$. We formulate and propose relations of these new classes of numbers with previous well-known numbers such as perfect, totient, triangular, pentagonal, and hexagonal numbers. These new classes of integers have been completely characterized. Finally, as an application of these new classes of numbers, a new graph labeling is also proposed on anti-totient numbers.
Keywords : Anti totient number, Half anti totient number, near Zumkeller number, half near Zumkeller number, graph labeling