Geodesic
Explicit Cayley covers of Kautz digraphs
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/592
Classification : 05E18, 05C25, 05C20 
@article{10_37236_592,
     author = {Josep M. Brunat},
     title = {Explicit {Cayley} covers of {Kautz} digraphs},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/592},
     zbl = {1220.05133},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/592/}
}
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Josep M. Brunat. Explicit Cayley covers of Kautz digraphs. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/592

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