Geodesic
On the existence of Frobenius digraphical representations
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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A Frobenius group is a transitive permutation group that is not regular and such that only the identity fixes more than one point. A digraphical, respectively graphical, Frobenius representation, DFR and GFR for short, of a Frobenius group $F$ is a digraph, respectively graph, whose automorphism group as a group of permutations of the vertex set is $F$. The problem of classifying which Frobenius groups admit a DFR and GFR has been proposed by Mark Watkins and Thomas Tucker and is a natural extension of the problem of classifying which groups that have a digraphical, respectively graphical, regular representation.In this paper, we give a partial answer to a question of Mark Watkins and Thomas Tucker concerning Frobenius representations: "All but finitely many Frobenius groups with a given Frobenius complement have a DFR".
DOI : 10.37236/7097
Classification : 05C25, 05C20, 20B25
Mots-clés : regular representation, Frobenius representation, Cayley digraph, automorphism group 
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     author = {Pablo Spiga},
     title = {On the existence of {Frobenius} digraphical representations},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {2},
     doi = {10.37236/7097},
     zbl = {1390.05095},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7097/}
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Pablo Spiga. On the existence of Frobenius digraphical representations. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7097

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