chromatic and clique numbers of a class of perfect graphs

Let p be a prime number and n be a positive integer. The graph Gp(n) is a graph with vertex set [n] = {1, 2, . . . , n}, in which there is an arc from u to v if and only if u ̸= v and p ∤ u + v. In this paper it is shown that Gp(n) is a perfect graph. In addition, an explicit formula for the chromatic number of such graph is given.