Let A be the adjacency matrix of a graph G = (V,E). Moreover, let A' = D number of zero entries in A'. Prove that G has 1+ V connected components. A' and let æ be the (Note: For matrices A, B of size m × n, A+ B is the m × n matrix with (A + B)ij = A¡j+ Bij) (Hint (part1): start by proving what A' ; represents (to get partial points).) (Hint (part2): assume there are 1 < k <|V| connected components and prove 1 + = k.)

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