Designs, Codes and Cryptography

, Volume 65, Issue 1, pp 65-69

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Spectral characterization of a graph on the flags of the eleven point biplane

  • A. BlokhuisAffiliated withEindhoven University of Technology
  • , A. E. BrouwerAffiliated withEindhoven University of Technology Email author 


We characterize a 55-point graph by its spectrum \({4^1, (-2)^{10}, (-1 \pm \sqrt{3})^{10}, ((3 \pm \sqrt{5})/2)^{12}}\) . No interlacing is used: examination of tr A m for m ≤ 7 together with study of the representation in the eigenspace for the eigenvalue −2 suffices.


Spectral characterization Euclidean representation Graph representation Iofinova-Ivanov graph

Mathematics Subject Classification (2000)

05C40 05Bxx 05Exx 05C38