[Solved] MA1971 Quiz 5

Show all work needed to reach your answers.

1. Please give the graph theory definition of a tree.
2. 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. 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.