Question: 4. Let G be a directed graph represented by the adjaceney matrix A. In directed graphs: A(mu) 1 if (u v) exists and A(u,u)-0 otherwise.

4. Let G be a directed graph represented by the adjaceney matrix A. In directed graphs: A(mu) 1 if (u v) exists and A(u,u)-0 otherwise. A tournament is a directed graph such that for any pair u u exactly one of (uv)or (vu) exists. An acyclic tournament is a tournament with no cycles. A source is a vertex whose in-degree is zero. A destination is a vertex whose out-degree is zero. (a) Describe an algorithm that checks if a directed graph G is a tournament. What is the complexity of your algorithm? Explain. (b) Prove that in an acyelic tournament there is exactly one source and one destination. Describe an efficient algorithm (O(n)-time) to find the source vertex of an acyclic tournament

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