Graph Reconstruction - Some New Developments*

Abstract

The reconstruction conjecture claims that every graph on at least three vertices is uniquely determined by its collection of vertex deleted subgraphs. Even though it is one of the foremost unsolved problems in Graph Theory, work on it has slowed down, may be due to the general feeling that existing techniques are not likely to lead to a complete solution. Here we give the results that have appeared recently in some selected variations of the reconstruction problem like edge reconstruction, degree associated reconstruction, vertex switching reconstruction and reconstruction numbers.