Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1: 34

Answer

The degree of vertex A is 2. The degree of vertex B is 2. The degree of vertex C is 5. The degree of vertex D is 3. The degree of vertex E is 1. The degree of vertex F is 3. The degree of vertex G is 2. The degree of vertex H is 2. The degree of vertex I is 2.

Work Step by Step

The degree of a vertex is the number of edges connected to that vertex. Vertex A has 2 edges connected to it, so the degree of vertex A is 2. Vertex B has 2 edges connected to it, so the degree of vertex B is 2. Vertex C has 3 edges connected to it. Vertex C also has a loop which adds 2 to the degree of the vertex. Therefore, the degree of vertex C is 5. Vertex D has 3 edges connected to it, so the degree of vertex D is 3. Vertex E has 1 edge connected to it, so the degree of vertex E is 1. Vertex F has 3 edges connected to it, so the degree of vertex F is 3. Vertex G has 2 edges connected to it, so the degree of vertex G is 2. Vertex H has 2 edges connected to it, so the degree of vertex H is 2. Vertex I has 2 edges connected to it, so the degree of vertex I is 2.
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