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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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)].
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)].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometric and Algebraic Combinatorics”.
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Blokhuis, A., Brouwer, A.E. Spectral characterization of a graph on the flags of the eleven point biplane. Des. Codes Cryptogr. 65, 65–69 (2012). https://doi.org/10.1007/s10623-011-9570-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-011-9570-5