Regularity of powers of edge ideals of Cohen-Macaulay weighted oriented forests

In this paper, we explicitly give combinatorial formulas for the regularity of powers of edge ideals, $\text{reg}(I(D{)}^k)$, of weighted oriented unmixed forests $D$ whose leaves are sinks ($V^{+}(D)$ are sinks). This combinatorial formula is a piecewise linear function of $k$, for $k\ge 1$.