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The graphs with all but two eigenvalues equal to $\pm 1$

Authors
  • Cioabă, Sebastian M.
  • Haemers, Willem H.
  • Vermette, Jason
  • Wong, Wiseley
Type
Preprint
Publication Date
Oct 24, 2013
Submission Date
Oct 24, 2013
Identifiers
arXiv ID: 1310.6529
Source
arXiv
License
Yellow
External links

Abstract

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.

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