Chromatic and clique numbers of a class of perfect graphs

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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.