Given a finite set $V$ and a set $S$ of permutations of $V$, the group action graph $mathrm{GAG}(V,S)$ is the digraph with vertex set $V$ and arcs $(v,v^sigma)$ for all $vin V$ and $sigmain S$. Let $langle Sangle$ be the group generated by $S$. The Cayley digraph $extrm{Cay}(langle Sangle, S)$ is called a Cayley cover of $mathrm{GAG}(V,S)$. We define the Kautz digraphs as group action graphs and give an explicit construction of the corresponding Cayley cover. This is an answer to a problem posed by Heydemann in 1996.
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机译：给定一个有限的集合$ V $和一个集合$ S $的$ V $排列，组动作图$ mathrm {GAG}（V，S）$是有顶点集合$ V $和弧线$（v ，v ^ sigma）$表示所有$ v in V $和$ sigma in S $。令$ langle S rangle $为$ S $生成的组。 Cayley有向图$ textrm {Cay}（ langle S rangle，S）$被称为$ mathrm {GAG}（V，S）$的Cayley封面。我们将Kautz有向图定义为组动作图，并给出相应Cayley覆盖的明确构造。这是对海德曼在1996年提出的问题的解答。
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