Designs, Codes and Cryptography

, Volume 65, Issue 1, pp 71–75

The graph with spectrum 141 240 (−4)10 (−6)9

  • Aart Blokhuis
  • Andries E. Brouwer
  • Willem H. Haemers
Open Access

DOI: 10.1007/s10623-011-9529-6

Cite this article as:
Blokhuis, A., Brouwer, A.E. & Haemers, W.H. Des. Codes Cryptogr. (2012) 65: 71. doi:10.1007/s10623-011-9529-6


We show that there is a unique graph with spectrum as in the title. It is a subgraph of the McLaughlin graph. The proof uses a strong form of the eigenvalue interlacing theorem to reduce the problem to one about root lattices.


Graph spectrum Strongly regular graph Root lattice 

Mathematics Subject Classification (2000)

05C50 05E30 05C62 
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Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Aart Blokhuis
    • 1
  • Andries E. Brouwer
    • 1
  • Willem H. Haemers
    • 2
  1. 1.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Econometrics & O.R.Tilburg UniversityTilburgThe Netherlands

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