Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 10 - Graphs and Trees - Exercise Set 10.1 - Page 640: 25

Answer

No such graph exists

Work Step by Step

Such a graph would have a total degree that is odd. Since each connection in a graph adds 1 to the degree of each node it connects for a total addition of 2 to the total degree, the total degree of a graph must always be even. The proposed graph has .a total degree of 27, which is impossible, so no such graph can exist.
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