Babai–Godsil–Imrich–Lovász conjecture on generic GRRs

Let $R$) be a group of order $n$ which is neither abelian nor generalised dicyclic. An inverse-closed subset $S$ of $R$ satisfies $s\in S\Rightarrow s^{-1}\in S$. A graphical regular representation (GRR) is a Cayley graph whose automorphism group is precisely the right-regular representation of $R$.

Babai–Godsil–Imrich–Lovász conjecture. The proportion of inverse-closed subsets $S$ of $R$ such that $\operatorname{Cay}(R,S)$ is a GRR goes to $1$ as $n\to\infty$.

The conjecture asserts that, apart from abelian and generalised dicyclic groups, almost every inverse-closed Cayley graph is a GRR. It was recently proved by Dobson and the last two authors, so its status is solved.