Explanation By definition, graph that has an edge between each pair of its vertices is called a completegraph. A Hamilton path that starts and ends at similar vertex and passes through all other vertices exactly once is called a Hamilton circuit. For a complete graph with n vertices, without the starting vertex of the graph there are n − 1 other vertices which are connected to each other. The total number of circuits would be the permutation of these n − 1 vertices among themselves

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Author: Blitzer

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Chapter 14.3, Problem 2CVC

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To fill: The blank in the provided statement, ‘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 ______.’

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Chapter 14.3, Problem 1CVC

Chapter 14.3, Problem 3CVC

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The blank in the provided statement, ‘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 ______ .’

Solution Summary: The author explains that a complete graph has an edge between each pair of its vertices, and the number of Hamilton circuits in the graph is given by the factorial expression ______.

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To fill: The blank in the provided statement, ‘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 ______.’

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Chapter 14 Solutions