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### 9.2 PATHS

##### Example 9.17.

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Consider the graph shown in Figure 9.19. Let us imagine that the vertices are towns and the edges are roads connecting them. It is clear that we can travel from a to B by road but there is no such roadway between D and H. To reach B from a, we take the following route: A to E via e _{3}.E to D via e _{4}.D to C via e _{5}.C to B via e _{6}.
## Figure 9.19.Naturally, we may represent the above route as . Further, is also a route between A and B. is also a route, perhaps roundabout, between A and B. Let us also note that is not a meaningful route at all, for E is not an end of e |

Definition 9.11: Let G be a graph and u, v be two vertices. A u - v walk in G is defined as a finite sequence