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1. (5 points) Please give the graph theory definition of a tree.
2. (5 points) Suppose that you have a friend who has taken a graph theory course and who claims to have drawn a tree with 15 vertices and 12 edges. In one sentence, please explain why is your friend mistaken.
3. (10 points) An edge in a connected graph G is a bridge iff its removal will disconnect the graph. Please show that if G is a cycle, then none of its edges is a bridge. Hint: Start with the definition of a cycle.