Could someone give me a hint for exercise 2.iii of these lecture notes? The exercise asks to show that a $k$-regular undirected graph (without loops) whose adjacency matrix $A$ has eigenvalues $k=\lambda_1(A) \geq \lambda_2(A) \geq \cdots \geq \lambda_n(A)$ satisfies $\max(|\lambda_2(A)|, |\lambda_n(A)|) \geq \sqrt{k} - o(1).$
Eigenvalues of regular graphs
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linear-algebra
graph-theory
eigenvalues-eigenvectors
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0Ah, yes. Thanks! – 2012-01-01