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Linear Algebra and Its Applications
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On graphs whose least eigenvalue exceeds - 1 - √2

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Abstract

Let G be a graph, A(G) its adjacency matrix. We prove that, if the least eigenvalue of A(G) exceeds -1 - √2 and every vertex of G has large valence, then the least eigenvalue is at least -2 and G is a generalized line graph. © 1997.

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