MA 1971 Bridge to Higher Mathematics
Quiz 5
Show all work needed to reach your answers.
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.
