Geodesic
Graphs with All But Two Eigenvalues In [−2, 0]
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 379-391

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The eigenvalues of a graph are those of its adjacency matrix. Recently, Cioabă, Haemers and Vermette characterized all graphs with all but two eigenvalues equal to −2 and 0. In this article, we extend their result by characterizing explicitly all graphs with all but two eigenvalues in the interval [−2, 0]. Also, we determine among them those that are determined by their spectrum.
Keywords: graph spectrum, complete multipartite graph, graph determined by its spectrum 
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     author = {Abreu, Nair and Alencar, Jorge and Brondani, Andr\'e and de Lima, Leonardo and Oliveira, Carla},
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Abreu, Nair; Alencar, Jorge; Brondani, André; de Lima, Leonardo; Oliveira, Carla. Graphs with All But Two Eigenvalues In [−2, 0]. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 2, pp. 379-391. http://geodesic.mathdoc.fr/item/DMGT_2020_40_2_a1/