Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Brouwer A.E., Haemers W.H.: Structure and uniqueness of the (81,20,1,6) strongly regular graph. Discrete Math. 106/107, 77–82 (1992)
Brouwer A.E., Cohen A.M., Neumaier A.: Distance-Regular Graphs. Springer, Heidelberg (1989)
van Dam E.R., Haemers W.H.: Which graphs are determined by their spectrum? Linear Algebra Appl. 373, 241–272 (2003)
van Dam E.R., Haemers W.H.: Developments on spectral characterizations of graphs. Discrete Math. 309, 576–586 (2009)
Cameron P.J., Goethals J.-M., Seidel J.J.: Strongly regular graphs having strongly regular subconstituents. J. Algebra 55, 257–280 (1978)
Haemers W.H.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 226–228, 593–616 (1995)
Weetman G.: Diameter bounds for graph extensions. J. Lond. Math. Soc. 50, 209–221 (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. & Haemers, W.H. The graph with spectrum 141 240 (−4)10 (−6)9 . Des. Codes Cryptogr. 65, 71–75 (2012). https://doi.org/10.1007/s10623-011-9529-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-011-9529-6