In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences as well as bounds on other orientations of oft studied tree topologies including generalized stars and caterpillars.

翻译：在本文中,我们证明每棵面向方向的树的主宰色谱数在方向逆转的情况下是无变的。除了这一标记结果外,我们还证明了芳香和反芳香色谱的精确支配色谱数,以及包括普通恒星和毛虫在内的经研究的树本学的其他方向的界限。