Designs, Codes and Cryptography

, Volume 65, Issue 1–2, pp 65–69

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

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 Am 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 

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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