On k-prime graphs

In the context of a simple undirected graph , a -prime labeling refers to assigning distinct integers from the set to its vertices, such that adjacent vertices in are labeled with numbers that are relatively prime to each other. If has a -prime labeling, we say that is a -prime graph ( -PG). In this article, we characterize when a graph up to order 6 is a -PG and characterize when a graph of order 7 is a -PG whenever and are not divisible by 5. Also, we find a lower bound for the independence number of a -PG. Finally, we study when a cycle is a -PG.