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: 51

Answer

The degree of vertex A, vertex C, and vertex D is 3. Vertex B has a degree of 5. Therefore, each vertex is an odd vertex. Since each vertex is odd, this is a graph with four odd vertices and one loop at vertex B.
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Work Step by Step

The degree of a vertex is the number of edges connected to the vertex. If the degree of a vertex is an odd number, then the vertex is an odd vertex. We can draw a graph with four vertices with edges AB, AC, AD, BD, CD, and BC. Then the degree of vertex A, vertex C, and vertex D is 3. Vertex B has a loop and a loop adds 2 to the degree of the vertex. Vertex B has a degree of 5. Therefore, each vertex is an odd vertex. Since each vertex is odd, this is a graph with four odd vertices and one loop at vertex B.
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