Prove Lemma 10.1.1(a): If G is a connected graph, then any two distinct vertices of G can be connected by a path. (You may use the result stated in exercise 43.)

To prove:

If G is a connected graph, then any two distinct vertices of G can be connected by a path.

Given information:

G is a connected graph.

Proof:

Let G be a connected graph and let u and v be two distinct vertices of G.

Since G is connected, there exists a walk W between u and v.

If W contains a repeated vertex v, then delete the part of the walk between the two occurrences of v and rename the resulting walk as W...