Reconstruction conjecture 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) 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 website also.