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Let $D$ be a strong balanced digraph on $2a$ vertices. Adamus et al. haveproved that $D$ is hamiltonian if $d(u)+d(v)\ge 3a$ whenever $uv\notin A(D)$and $vu\notin A(D)$. The lower bound $3a$ is tight. In this paper, we shallshow that the extremal digraph on this condition is two classes of digraphsthat can be clearly characterized. Moreover, we also show that if$d(u)+d(v)\geq 3a-1$ whenever $uv\notin A(D)$ and $vu\notin A(D)$, then $D$ istraceable. The lower bound $3a-1$ is tight.

Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs