Counting graphs with diameter d - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T16:13:56Z http://mathoverflow.net/feeds/question/109482 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109482/counting-graphs-with-diameter-d Counting graphs with diameter d nomatter 2012-10-12T19:19:18Z 2012-10-12T23:32:13Z <p>Is there some known sequence which gives me the number of graphs with diameter d?</p> <p>Similarly is there some 2D-sequence which gives me the number of graphs with n vertices and diameter d?</p> <p>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": <a href="http://algo.inria.fr/flajolet/Publications/books.html" rel="nofollow">http://algo.inria.fr/flajolet/Publications/books.html</a></p> http://mathoverflow.net/questions/109482/counting-graphs-with-diameter-d/109500#109500 Answer by Brendan McKay for Counting graphs with diameter d Brendan McKay 2012-10-12T23:32:13Z 2012-10-12T23:32:13Z <p>The asymptotic number of graphs with given order and diameter was determined recently by Zoltán Füredi and Younjin Kim, see <a href="http://arxiv.org/abs/1204.4580" rel="nofollow">http://arxiv.org/abs/1204.4580</a> . I don't think there is much prospect of finding generating functions.</p>