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Let G be a connected graph with n nodes. Define L R nn the associate Laplacian matrix and 1 2 n, its eigenvalues. Let G'

Let G be a connected graph with n nodes. Define L Rnn the associate Laplacian matrix and 1 2 n, its eigenvalues. Let G' be a graph constructed from G by simply adding an edge. Similarly denote by '2 its second smallest eigenvalue. Show that '2 2.

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