Question: Let A be the adjacency matrix of a graph G a. By induction, prove that for all n 1, the (i, j) entry of

Let A be the adjacency matrix of a graph G
a. By induction, prove that for all n ≥ 1, the (i, j) entry of A" is equal to the number of n-paths between vertices i and j.
b. How do the statement and proof in part (a) have to be modified if G is a digraph?

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