2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 383388
author:  Manuel Bodirsky, Omer Giménez, Mihyun Kang and Marc Noy 

title:  On the number of series parallel and outerplanar graphs 
keywords:  Series parallel graph, outerplanar graph, random graph, asymptotic enumeration, limit law, normal law, analytic combinatorics. 
abstract: 
We show that the number
g
of labelled seriesparallel graphs on
n
n
vertices is asymptotically
g
, where
n
∼g·n
5/2
γ
n
n!
γ
and
g
are explicit computable constants. We show that the
number of edges in random seriesparallel 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.

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reference:  Manuel Bodirsky and Omer Giménez and Mihyun Kang and Marc Noy (2005), On the number of series parallel and outerplanar graphs , in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 383388 
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