A walk with no arc repeated which begins and ends with forward arcs, in which the arcs alternate between forward and backward arcs, is called forward antidirected trail. A digraph D with order at least three containing a forward antidirected (x, y)-trail for every pair of distinct vertices x, y of D is antistrong. In this paper, we show that the Cartesian product of two antistrong digraphs is antistrong. Moreover, one of the results is that the Lexicographic product of an antistrong digraph and a digraph is antistrong. Finally, the subject is researched to give a necessary and sufficient condition to decide whether a tournament is antistrong.

以向前弧线开始和结束的没有重复弧线的行走，其中弧线在向前和向后弧线之间交替，称为向前反向轨迹。有向图d与顺序至少三个含有向前antidirected（X，  ÿ）-TRAIL对于每对独特的顶点的X，ÿ的d被antistrong。在本文中，我们证明了两个反强有向图的笛卡尔积是反强的。此外，结果之一是Lexicographic 产品一个反强有向图和一个有向图是反强的。最后，对本题进行了研究，给出了判断比赛是否为反强的充要条件。