We give a complete answer to the GFR conjecture, proposed by Conder, Doyle, Tucker and Watkins: “All but finitely many Frobenius groups $F=N⋊H$ with a given complement H have a GFR, with the exception when $|H|$ is odd and N is Abelian but not an elementary 2-group”. Actually, we prove something stronger, we enumerate asymptotically GFRs; we show that, besides the exceptions listed above, as $|N|$ tends to infinity, the proportion of GFRs among all Cayley graphs over N containing F in their automorphism group tends to 1.

中文翻译：

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关于图形Frobenius表示的存在及其渐近枚举

对于康德（Conder），道尔（Doyle），塔克（Tucker）和沃特金斯（Watkins）提出的GFR猜想，我们给出了完整的答案： $F=ñ⋊H$给定补码H的GFR，但当$|H|$是奇数，N是阿贝尔语，但不是基本2组”。实际上，我们证明了一些更强的东西，我们渐近地列举了GFR。我们证明，除了上面列出的例外情况，$|ñ|$趋于无穷大，自同构组中所有Cayley图中的GFR占含N的F的比例趋于1。