Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - Chapter 14 Test: 3

Answer

The paths B,C,E,D and B,A,D,E,C are two paths which start at vertex B and pass through vertex E.

Work Step by Step

If there is at least one edge connecting two vertices in a graph, the vertices are adjacent to each other. A path is a sequence of adjacent vertices. If a path passes through a vertex, then the vertex is part of the path, but the vertex is not one of the endpoints of the path. Let's start at vertex B. The path can travel to vertex C, then to vertex E, and then to vertex D. This path is B,C,E,D. This path starts at vertex B and passes through vertex E. Let's start at vertex B. The path can travel to vertex A, then to vertex D, then to vertex E, and then to vertex C. This path is B,A,D,E,C. This path starts at vertex B and passes through vertex E. The paths B,C,E,D and B,A,D,E,C are two paths which start at vertex B and pass through vertex E.
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