The number of \(h\)-strongly connected digraphs with small diameter (Q2760453)

Author proves that the number of \(h\)-strongly connected digraphs of order \(n\) and diameter \(d\) is: NEWLINE\[NEWLINE\begin{aligned} 4^{{n\choose 2}}(3/4 + o(1))^n\;&\text{for }d= 3\text{ and every fixed }h\geq 1,\tag{i}\\ 4^{{n\choose 2}}(2^{- h-2}+ 2^{-2}+ o(1))^n\;&\text{for }d= 4\text{ and every fixed }h\geq 2,\tag{ii}\\ 4^{{n\choose 2}}((2^{h+ 1}- 1)2^{- kh+ 3h-2}+ o(1))^n\;&\text{for }d\geq 5\text{ and every fixed }h\geq 1.\tag{iii}\end{aligned}NEWLINE\]NEWLINE{}.