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The graphs with all but two eigenvalues equal to $\pm 1$

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Preprint
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Submission Date
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arXiv ID: 1310.6529
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arXiv
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Abstract

We determine all graphs whose adjacency matrix has 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.

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