3 problems

Existence conjecture for divisible design Cayley digraphs with prime-power parameters
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…
opencayley-digraphs design-theory finite-fields
0 responses
06
The closedness and value conjecture for the degree-three density constant
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…
opencayley-digraphs extremal-combinatorics finite-abelian-groups
0 responses
06
The classification conjecture for groups admitting oriented regular representations
The ORR classification conjecture. Every finite group $G$ admits an ORR, unless one of the following occurs:
opencayley-digraphs finite-groups graph-automorphisms
0 responses
03

Existence conjecture for divisible design Cayley digraphs with prime-power parameters