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Abstract
The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers, Vermette and Wong characterized all connected non-bipartite graphs with all but two eigenvalues equal to 1 or . In this article, we will generalize their result by explicitly determining all connected non-bipartite graphs with all but two eigenvalues in the interval
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Acknowledgements
The second author would like to thank PNPD–CAPES for the support received during 2014. He is also very grateful to the Department of Production Engineering at CEFET/RJ for the excellent hospitality during the time of his stay in Brazil.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico [309723/2015-9].