Explicit Cayley Covers of Kautz Digraphs

Josep M. Brunat

Abstract


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 $v\in V$ and $\sigma\in S$. Let $\langle S\rangle$ be the group generated by $S$. The Cayley digraph $\textrm{Cay}(\langle S\rangle, S)$ 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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