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Linear and Multilinear Algebra Volume 65, 2017 - Issue 3
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Articles

The non-bipartite graphs with all but two eigenvalues in [–1, 1]

L. S. de LimaDepartamento de Engenharia de Produção, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ), Rio de Janeiro, Brazil.Correspondence[email protected]
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,
A. MohammadianDepartamento de Engenharia de Produção, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ), Rio de Janeiro, Brazil.View further author information
&
C. S. OliveiraDepartamento de Matemática, Escola Nacional de Ciências Estatísticas (ENCE-IBGE), Rio de Janeiro, Brazil.View further author information
Pages 526-544 | Received 09 Nov 2015, Accepted 24 May 2016, Published online: 13 Jun 2016

References

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  • Torgašev A. Graphs whose second least eigenvalue is greater than -1. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 1982;735–762:148–154.
  • Smith JH. Some properties of the spectrum of a graph. Combinatorial structures and their applications. New York (NY): Gordon and Breach; 1970. p. 403–406.
  • van Dam ER, Spence E. Combinatorial designs with two singular values–I: uniform multiplicative designs. J. Combin. Theory Ser. A. 2004;107:127–142.
  • Cioabă SM, Haemers WH, Vermette JR, Wong W. The graphs with all but two eigenvalues equal to ±1. J. Algebraic Combin. 2015;41:887–897.
  • Petrovi\’{c} M. On graphs with exactly one eigenvalue less than -1. J. Combin. Theory Ser. B. 1991;52:102–112.
  • Neumaier A. The second largest eigenvalue of a tree. Linear Algebra Appl. 1982;46:9–25.
  • Brouwer AE, Haemers WH. Spectra of graphs. New York (NY): Springer; 2012.

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