Description
Speaker: Willem H. Haemers
Tilburg University, The Netherlands
Title: Are almost all graphs determined by their spectrum?
Abstract: An important class of problems in mathematics deals with the reconstruction of a
structure from the eigenvalues of an associated matrix. The most famous such prob-
lem is: ‘Can one hear the shape of a drum?’. Here we deal with the question: ‘Which
graphs are determined by the spectrum (eigenvalues) of its adjacency matrix’? More
in particular we ask ourselves whether this is the case for almost all graphs. There
is no consensus on what the answer should be, although there is a growing number
of experts that expect it to be affirmative. In this talk we will present several re-
sults related to this question. This includes constructions of cospectral graphs and
characterizations of graphs by their spectrum. Some of these results support an
affirmative answer, some support the contrary. It will be explained why the speaker
believes that it is true.