abstract
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Reconstruction of weighted graphs by their spectrum

Lorenz Halbeisen and Norbert Hungerbühler

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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.