The number of edges in critical strongly connected graphs (Q5936056)

A directed graph is called critical strongly connected if it is strongly connected, i.e., each vertex is reachable from every other vertex, and if the removal of any vertex results in a non-strongly connected digraph. It is proved that the maximum number of directed edges in a critical strongly connected digraph on \(n\) vertices (\(n \geq 4\)) is \({n \choose 2} -n+4\).