On the number of series parallel and outerplanar graphs

We show that the number gn of labelled series-parallel graphs on n vertices is asymptotically gn g · n 5/2 n n!, where and g are explicit computable constants. We show that the number of edges in random series-parallel graphs is asymptotically normal with linear mean and variance, and that the number of edges is sharply concentrated around its expected value. Similar results are proved for labelled outerplanar graphs.