Question: 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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