Bosák's classification conjecture for mixed Moore graphs

Let $d\geq 1$ and $k\geq 3$ be integers. A mixed Moore graph is a finite graph attaining the mixed Moore bound for degree $d$ and diameter $k$; write $\vec{C}_{k+1}$ for the directed cycle of length $k+1$ and $C_{k+1}$ for the undirected cycle of length $k+1$.

Bosák's conjecture. A finite graph $G$ is a mixed Moore graph of degree $d$ and diameter $k$ if and only if either $d=1$ and $G$ is $\vec{C}_{k+1}$, or $d=2$ and $G$ is $C_{k+1}$.

The conjecture classifies mixed Moore graphs of diameter at least three. It was proposed by Bosák in 1979 and proved in 2007 by Nguyen, Miller and Gimbert.