Geodesic
The graphs with all but two eigenvalues equal to $\pm 1$
Journal of Algebraic Combinatorics, Tome 41 (2015) no. 3, pp. 887-897.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We determine all graphs whose adjacency matrices have at most two eigenvalues (multiplicities included) different from $\pm 1$ and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen.
Classification : 05C50, 05B20
Keywords: adjacency matrix, friendship graph, spectral characterization 
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     title = {The graphs with all but two eigenvalues equal to $\pm 1$},
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Cioabă, Sebastian M.; Haemers, Willem H.; Vermette, Jason R.; Wong, Wiseley. The graphs with all but two eigenvalues equal to $\pm 1$. Journal of Algebraic Combinatorics, Tome 41 (2015) no. 3, pp. 887-897. http://geodesic.mathdoc.fr/item/JAC_2015__41_3_a1/