Explicit Cayley covers of Kautz digraphs (Q540110)

Summary: Given a finite set \(V\) and a set \(S\) of permutations of \(V\), the group action graph \(\text{GAG}(V, S)\) is the digraph with vertex set \(V\) and arcs \((v, v^\sigma)\) for all \(v\in V\) and or \(\sigma\in S\). Let \(\langle S\rangle\) be the group generated by \(S\). The Cayley digraph \(\text{Cay}(\langle S\rangle, S)\) is called a Cayley cover of \(\text{GAG}(V, S)\). 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 \textit{Heydemann} in 1996.