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Chapter 14: Problem 15

In Exercises 15-18, determine the number of Hamilton circuits in a complete graph with the given number of vertices. 3

Short Answer

Expert verified
The number of Hamilton circuits in the graph is 2.

Step by step solution

01

Identify the number of vertices

From the exercise, it can be seen that the number of vertices in the graph is 3.
02

Input Into the Formula

The formula to determine the number of Hamilton circuits in a complete graph is \(N = (n-1)!\). Substituting n = 3 into the formula, we get: \(N = (3-1)!\)
03

Compute the Factorial Value

Find the factorial of the result from the previous step, \(2!\), which equals 2. This result is the total number of Hamilton circuits in the graph.

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Most popular questions from this chapter

In Exercises 49-52, draw a graph with the given characteristics. The graph has four odd vertices and at least one loop.

Draw a graph with six vertices and two bridges.

In Exercises 13-18, a connected graph is described. Determine whether the graph has an Euler path (but not an Euler circuit), an Euler circuit, or neither an Euler path nor an Euler circuit. Explain your answer. The graph has 80 even vertices and no odd vertices.

In your own words, briefly describe how to find the minimum spanning tree using Kruskal's Algorithm.

. What is a Hamilton circuit? How does this differ from an Euler circuit?
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