Thinking Mathematically (6th Edition)

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

Chapter 14 - Graph Theory - Chapter Summary, Review, and Test - Review Exercises: 25

Answer

(a) The graph is a complete graph so it must have Hamilton circuits. (b) This graph has 6 Hamilton circuits.

Work Step by Step

(a) A graph that has an edge between each pair of its vertices is called a complete graph. If such a graph has $n$ vertices, the number of Hamilton circuits in the graph is given by the factorial expression $(n-1)!$. The graph in this exercise is a complete graph so it must have Hamilton circuits. (b) This graph is a complete graph with 4 vertices. The number of Hamilton circuits is $(4-1)! = 3! = 6$. This graph has 6 Hamilton circuits.
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