Question: 7. Prove that every connected graph has a vertex whose removal (includ- ing all adjacent edges) will not disconnect the graph, and write a DFS

7. Prove that every connected graph has a vertex whose removal

7. Prove that every connected graph has a vertex whose removal (includ- ing all adjacent edges) will not disconnect the graph, and write a DFS method that finds such a vertex. Hint : Consider a vertex whose adja- cent vertices are all marked. [6 marks] 2 8. Explain why the following algorithm does not necessarily produce a topological order: Run BFS, and label the vertices by increasing dis- tance to their respective source. [6 marks]

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