October 2012, Volume 65, Issue 1-2, pp 71-75,
Open Access This content is freely available online to anyone, anywhere at any time.
The graph with spectrum 141 240 (−4)10 (−6)9
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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.
This is one of several papers published together in Designs, Codes and Cryptography on the special topic: “Geometric and Algebraic Combinatorics”.
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- 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) CrossRef
- Cameron P.J., Goethals J.-M., Seidel J.J.: Strongly regular graphs having strongly regular subconstituents. J. Algebra 55, 257–280 (1978) CrossRef
- Haemers W.H.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 226–228, 593–616 (1995) CrossRef
- Weetman G.: Diameter bounds for graph extensions. J. Lond. Math. Soc. 50, 209–221 (1994)
- The graph with spectrum 141 240 (−4)10 (−6)9
- Open Access
- Available under Open Access This content is freely available online to anyone, anywhere at any time.
Designs, Codes and Cryptography
Volume 65, Issue 1-2 , pp 71-75
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- Graph spectrum
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