Designs, Codes and Cryptography

, Volume 65, Issue 1, pp 71–75

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


  • Aart Blokhuis
    • Department of MathematicsEindhoven University of Technology
  • Andries E. Brouwer
    • Department of MathematicsEindhoven University of Technology
    • Department of Econometrics & O.R.Tilburg University

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

Open Access

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Copyright information

© The Author(s) 2011