Novel Classes of Integers and Their Applications in Graph Labeling

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