The edge-reconstruction number ern(G) of a graph G is equal to the minimum number of edge-deleted subgraphs G−e of G which are sufficient to
determine G up to isomorphism. Building upon the work of Molina and
using results from computer searches by Rivshin and more recent ones
which we carried out, we show that, apart from three known exceptions,
all bicentroidal trees have edge-reconstruction number equal to 2. We
also exhibit the known trees having edge-reconstruction number equal to
3 and we conjecture that the three infinite families of unicentroidal trees
which we have found to have edge-reconstruction number equal to 3 are
the only ones.peer-reviewe
