Maximal Eulerian directed graph with specified degree and diameter

We have obtained the maximum size of the Eulerian directed graph without -2 cycle with order n and diameter d for d=2 and d=3. We have also proven that if n≥5 and n-d is odd, the maximum size of such a graph is d-2+((n-d+2)(n-d+1))/2. We have also built graphs with such parameters. We have also proved that if n-d is even, the maximum size of such a graph is not less than d-2+((n-d)(n-d+2))/2. By making graphs with these parameters, we have shown that this low bound is achievable.