Question: When an adjacency-matrix representation is used, most graph algorithms require time (V2), but there are some exceptions. Show that determining whether a directed graph G

When an adjacency-matrix representation is used, most graph algorithms require time Ω (V2), but there are some exceptions. Show that determining whether a directed graph G contains a universal sink-a vertex with in-degree |V| - 1 and out-degree 0-can be determined in time O (V), given an adjacency matrix for G.

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We start by observing that if aij 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 ... View full answer

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