Is there some known sequence which gives me the number of graphs with diameter d?


Similarly is there some 2D-sequence which gives me the number of graphs with n vertices and diameter d?


If there is no closed form is there some way to study this problem in terms of generating function and apply to it some asymptotic analysis like in "Analytic Combinatorics": <http://algo.inria.fr/flajolet/Publications/books.html>



Counting graphs with diameter d
The asymptotic number of graphs with given order and diameter was determined recently by Zoltán Füredi and Younjin Kim, see <http://arxiv.org/abs/1204.4580> . I don't think there is much prospect of finding generating functions.


