Coprime divisors graphs and their coloring parameters

Let n be a composite integer.The coprime divisors graph of n, denoted by Γn, is the graph whose vertices are the proper divisors of n and two vertices are adjacent if they are coprime.In this paper, we study the structure of Γn and its coloring parameters.Indeed, we give the explicit forms of the degrees, distances, diameter, and girth of this graph.We also compute explicitly the clique number, the chromatic number, and the independence number of Γn.Moreover, we prove that Γn is a perfect graph.