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Properties of Graphs with an eigenvalue of -1 (adjacency matrix)?

I am wondering if there are special classes of graphs that have eigenvalue of -1 for the adjacency matrix. I know that the complete graphs, Kn, have this property, but am wondering if other graphs do ...
dan's user avatar
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5 answers
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The middle eigenvalues of an undirected graph

Let $ \lambda_1 \ge \lambda_2 \ge \dots \ge \lambda_{2n} $ be the collection of eigenvalues of an adjacency matrix of an undirected graph $G$ on $2n$ vertices. I am looking for any work or references ...
Tomaž Pisanski's user avatar

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