We investigate infinite highly-arc-transitive digraphs with two additional properties, property Z and descendant-homogeneity. We show that if D is a highly-arc-transitive descendant-homogeneous digraph with property Z and F is the subdigraph spanned by the descendant sets of a line in D, then F is a locally finite 2-ended digraph with property Z. If, moreover, D has prime out-valency, then there is only one possibility for the subdigraph F. This knowledge is then used to classify the highly-arc-transitive descendant-homogeneous digraphs of prime out-valency with property Z.

中文翻译：

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具有有限出价的高弧传递和后代齐次有向图

我们研究了具有两个附加属性的无限高弧传递有向图，属性 Z 和后代同质性。我们证明如果 D 是一个具有 Z 属性的高度弧传递后代齐次有向图，F 是 D 中一条线的后代集所跨越的子图，那么 F 是一个具有 Z 属性的局部有限二端有向图。如果，而且，D 有质外价，那么子图 F 只有一种可能性。 然后使用该知识对具有性质 Z 的质外价的高弧传递后代齐次有向图进行分类。