Divisor orientations of powers of paths and powers of cycles

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover, for odd n with 2k + 2 < n < 2k + bk2 c+ 3, we show that the graph C k n is not a divisor graph.