7 problems

Babai–Godsil conjecture. As the order of $G$ grows, almost all finite Cayley digraphs of $G$ are DRRs.

A unit circulant digraph of order $n$ is a Cayley digraph ${\rm Cay}({\mathbb Z}_n,S)$, where $S\subseteq{\mathbb Z}_n^*$ is the set of units in ${\mathbb Z}_n$. Toida's conjecture…

Converse conjecture. If a dihedral group of order $2n$ has $n=2$ or $n$ odd and square-free, then it is a DCI-group.

Let $G$ be a finite group and consider normal Cayley digraphs over $G$, meaning Cayley digraphs whose right-regular subgroup $G_r$ is normal in their automorphism group. A Cayley d…

Let $n$ be an odd prime power. A divisible design Cayley digraph is a Cayley digraph that forms a divisible design with parameters $(v,k,\lambda_1,\lambda_2,m,n)$, where the parame…

Let $d$ denote the degree of a Cayley digraph, and let $Delta_3$ and $Delta_3'$ be the associated density constants introduced in the paper. Degree-three density conjecture. The de…

The ORR classification conjecture. Every finite group $G$ admits an ORR, unless one of the following occurs: