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Let G be a connected graph of order n and A = A(G) be its adjacency matrix. 1. Prove that A(G) is an eigenvalue

Let G be a connected graph of order n and A = A(G) be its adjacency matrix. 1. Prove that A(G) is an eigenvalue of A if and only if G is regular. 2. Prove that if-A(G) is an eigenvalue of A, then G is regular and bipartite.

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