3. Consider a simple, undirected graph G and its adjacency matrix A. (a) What does the...

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3. Consider a simple, undirected graph G and its adjacency matrix A. (a) What does the sum of a row of A tell us about the corresponding vertex? (b) Suppose that G is d-regular (all vertices have degree d). Prove that d is an eigenvalue of A with the associated eigenvector [1,1, ..,1]T. 3. Consider a simple, undirected graph G and its adjacency matrix A. (a) What does the sum of a row of A tell us about the corresponding vertex? (b) Suppose that G is d-regular (all vertices have degree d). Prove that d is an eigenvalue of A with the associated eigenvector [1,1, ..,1]T.