Unique subgraphs and symmetrization

Investigations by P. Erdös, A. Rényi, A.E. Brouwer and others are continued. Graphs with the property that deletion of at most r edges produce distinct subgraphs are examined. A related problem is to determine the minimum number of adjacencies which must be altered in a grpha to change it into a symmetric graph, e.e. a graph with a nontrivial automorphism. Joint work with Zsolt Tuza, Hungarian Academy of Sciences and University of Veszprém.