   Chapter 10.1, Problem 47ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Prove that if there is a trail in a graph G from a vertex v to a vertex w, then there is a trail from w to v.

To determine

Prove that if there is a trail in a graph G from a vertex v to a vertex w, then there is a trail from w to v.

Explanation

Given information:

there is a trail in a graph G from a vertex v to a vertex w.

Proof:

Let v and w be vertices from the graph G and let ve1v1e2v2...vn1enw be a trail from vertex v to w (for some nonnegative integer n ).

Since ve1v1e2v2...vn1enw is a trial, ve1v1e2v2...vn1enw contains no repeated edges.

If v = w, then v is a trail from vertex w to vertex v (note that the trail cannot contain any repeated edges as it does not contain any edges).

If vw, then wenvn1en1

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