The paper "Enumeration and limit laws of series-parallel graphs" by Manuel Bodirsky, Omer Gimenez, Mihyun Kang, and Marc Noy, establishes that the number of labeled series-parallel graphs on $n$ vertices is asymptotically $$ g \cdot n^{-\frac{5}{2}} \gamma^n n! $$ where $g$ and $\gamma$ are constants. Perhaps you can convert their bound to one for unlabeled graphs (by removing the $n!$ factor) in terms of edges.
|
2 | added 30 characters in body | ||
|
|
||||
|
|
1 |
|
||
|
The paper "Enumeration and limit laws of series-parallel graphs" by Manuel Bodirsky, Omer Gimenez, Mihyun Kang, and Marc Noy, establishes that the number of labeled series-parallel graphs on $n$ vertices is asymptotically $$ g \cdot n^{-\frac{5}{2}} \gamma^n n! $$ where $g$ and $\gamma$ are constants. Perhaps you can convert their bound to one for unlabeled graphs in terms of edges. |
||||
