Question: Most graph algorithms that take an adjacency-matrix representation as input require time (V 2 ), but there are some exceptions. Show how to determine whether

Most graph algorithms that take an adjacency-matrix representation as input require time Ω(V²), but there are some exceptions. Show how to determine whether a directed graph G contains a universal sink-a vertex with in-degree |V| - 1 and out-degree 0-in time O(V), given an adjacency matrix for G.

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We start by observing that ifa ij 1 so that I j E then vertex i cannot be a universal sink for it has an outgoing edge Thus if row i contains a 1 then vertex i cannot be a universal sink This observat... View full answer

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