2. Does each of these lists of vertices form a path in the following graph? Which paths are simple? Which are cir- cuits

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2. Does each of these lists of vertices form a path in the following graph? Which paths are simple? Which are cir- cuits? What are the lengths of those that are paths? a) a, b, e, c, b b) a, d,a,d, a c) a, d, b, e, a d) a, b, e,c, b, d, a e

In Exercises 3-5 determine whether the given graph is con- nected. T 4.

18. Show that all vertices visited in a directed path connecting two vertices in the same strongly connected component of a directed graph are also in this strongly connected component.

19. Find the number of paths of length n between two differ- ent vertices in K4 if n is a) 2. b) 3. c) 4. d) 5. 24. Find the number of paths of length n between any two ad- jacent vertices in K3.3 for the values of n in Exercise 19.