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 - Page 902: 50

Answer

We can draw a graph with six vertices with edges AB, AC, BD, CD, AE, BE, EF, CF, and DF. Then the degree of each vertex is 3, so each vertex is an odd vertex. Since each vertex is odd, this is a graph with six odd vertices.
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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 six vertices with edges AB, AC, BD, CD, AE, BE, EF, CF, and DF. Then the degree of each vertex is 3, so each vertex is an odd vertex. Since each vertex is odd, this is a graph with six odd vertices.
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