[Reconstruction conjecture][1] says that graphs (with at least three vertices) are determined uniquely by their vertex deleted subgraphs. This conjecture is five decades old.

Searching relevant literature, I found that the following classes of graphs are known to be reconstructible :

 - trees
 - disconnected graphs, graphs whose complement is disconnected
 - regular graphs
 - Maximal Outerplanar Graphs
 - maximal planar graphs
 - outerplanar graphs
 - Critical blocks
 - Separable graphs without end vertices
 - unicyclic graphs (graphs with one cycle)
 - non-trivial cartesian product graphs
 - squares of trees
 - bidegreed graphs
 - unit interval graphs
 - threshold graphs
 - nearly acyclic graphs (i.e., G-v is acyclic)
 - cacti graphs
 - graphs for which one of the vertex deleted graph is a forest.

I recently proved that a special case of partial 2-trees are reconstructible. I am wondering if partial 2-trees (a.k.a [series-parallel graphs][2]) are known to be reconstructible. Partial 2-trees do not seem to fall into any of the above mentioned categories.

 - Am I missing any other known classes of reconstructible graphs in the above list ?
 - In particular, are partial 2-trees known to be reconstructible ?

I asked this [question at cstheory][3] website also.


  [1]: http://garden.irmacs.sfu.ca/?q=op/reconstruction_conjecture
  [2]: http://en.wikipedia.org/wiki/Series-parallel_graph
  [3]: https://cstheory.stackexchange.com/questions/5155/reconstruction-conjecture-and-partial-2-trees