Graph 1 is not a caterpillar.
Graph 2 is a caterpillar.
Graph 3 is not a caterpillar.
Graph 4 is not a caterpillar.
Graph 5 is not a caterpillar.
Graph 6 is not a caterpillar.
Graph 7 is a caterpillar.
Graph 8 is not a caterpillar.
Graph 9 is not a caterpillar.