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Designs, Codes and Cryptography

, Volume 65, Issue 1–2, pp 65–69 | Cite as

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

  • A. Blokhuis
  • A. E. BrouwerEmail author
Open Access
Article

Abstract

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.

Keywords

Spectral characterization Euclidean representation Graph representation Iofinova-Ivanov graph 

Mathematics Subject Classification (2000)

05C40 05Bxx 05Exx 05C38 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. Ivanov A.A.: Computations of lengths of orbits of a subgroup in a transitive permutation group. In: Faradžev I.A., Ivanov A.A., Klin M.H., Woldar A.J. (eds.) Methods of Complex Systems Study, pp. 3–8. Institute for System Studies, Moscow (1983) (Russian) [Translation in Investigations in Algebraic Theory of Combinatorial Objects, pp. 275–282. Kluwer, Dordrecht (1994)].Google Scholar
  2. Ivanov A.A., Iofinova M.E.: Bi-primitive cubic graphs. In: Investigations in the Algebraic Theory of Combinatorial Objects, pp. 123–134. Institute for System Studies, Moscow (1985) (Russian) [Translation pp. 459–472, Kluwer, Dordrecht (1994)].Google Scholar

Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Eindhoven University of TechnologyEindhovenThe Netherlands

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