abstract
Reconstruction of weighted graphs by their spectrum
Lorenz Halbeisen and Norbert Hungerbühler
It will be shown that for almost all weights one can reconstruct a
weighted graph from its spectrum. This result is the opposite to the
well-known theorem of Botti and Merris which states that
reconstruction of non-weighted graphs is in general impossible since
almost all (non-weighted) trees share their spectrum with another
nonisomorphic tree.