Data Structures, Algorithms, & Applications in C++
Chapter 16, Exercise 1

(a)

6,1,2,7,4 is a path in the graph and no vertex is repeated. So it is a simple path.

(b)

1,2,3,4 is not a path in the graph because (3,4) is not an edge of the graph. Therefore, it is not a simple path.

(c)

Even though 7,2,3,2,1,6 is a path in the graph, it is not a simple path because vertex 2 which is an interior path vertex is repeated.

(d)

4,5,7,2 is not a path in the graph because (4,5) is not an edge of the graph. Therefore, it is not a simple path.