I saw a question on the nauty emailing list without receiving any response, and it's something I've encountered in my own research as well. **I am currently interested in graphs with diameter 3.**

I would like to generate all graphs on 12 vertices with a fixed diameter using geng. Since when n>11, the number of graphs is too high and using pickg to collect the graphs with given diameter after generating 12 vertices connected graphs taking a long time. (By Suresh E)

For instance, maybe we want to obtain non-isomorphic graphs of order 20 with diameter 3. Perhaps they are not too many, one can hope. The numbers are not documented by Oeis. I just see this Number of trees of diameter 4.

Furthermore, I found a similar but not same question, since the user *nomatter* just concern about counting not generating:
Counting graphs with diameter d