The graphs with all but two eigenvalues equal to - 2 or 0

Sebastian M. Cioabă, Willem H. Haemers, Jason R. Vermette

Research output: Contribution to journalArticleScientificpeer-review

19 Citations (Scopus)


We determine all graphs whose adjacency matrix has at most two eigenvalues (multiplicities included) different from $\pm 1$ and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen.
Original languageEnglish
Pages (from-to)153-163
JournalDesigns Codes and Cryptography
Issue number1-2
Publication statusPublished - 1 Jul 2017


  • Adjacency matrix
  • Graph spectrum
  • Spectral characterizations


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