Developments on Spectral Characterizations of Graphs

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Abstract

In [E.R. van Dam and W.H. Haemers, Which graphs are determined by their spectrum?, Linear Algebra Appl. 373 (2003), 241-272] we gave a survey of answers to the question of which graphs are determined by the spectrum of some matrix associated to the graph. In particular, the usual adjacency matrix and the Laplacian matrix were addressed. Furthermore, we formulated some research questions on the topic. In the meantime some of these questions have been (partially) answered. In the present paper we give a survey of these and other developments.2000 Mathematics Subject Classification: 05C50
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages17
Volume2007-33
Publication statusPublished - 2007

Publication series

NameCentER Discussion Paper
Volume2007-33

Keywords

  • Spectra of graphs
  • Cospectral graphs
  • Generalized adjacency matrices
  • Distance-regular graphs

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