Reconstruction of Weighted Graphs by their Spectrum

Authors: Halbeisen L.¹; Hungerbühler N.²

Source: European Journal of Combinatorics, Volume 21, Number 5, July 2000 , pp. 641-650(10)

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Abstract:

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 non-isomorphic tree.Copyright 2000 Academic Press

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, U.C. Berkeley, Evans Hall 938, Berkeley, CA 94720, U.S.A. 2: Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, Leipzig, 04103, Germany

Publication date: 2000-07-01