The graphs with all but two eigenvalues equal to $-2$ or $0$

preprint2016arXivOpen access

We determine all graphs for which the adjacency matrix has at most two eigenvalues (multiplicities included) not equal to $-2$ , or $0$ , and determine which of these graphs are determined by their adjacency spectrum.

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The graphs with all but two eigenvalues equal to $-2$ or $0$

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The graphs with all but two eigenvalues equal to −2-2−2 or 000

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The graphs with all but two eigenvalues equal to $-2$ or $0$