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