Explanation Hamilton path: A path that passes through all the vertices of a graph exactly once is called a Hamilton path. Hamilton circuit: If a Hamilton path begins and ends at the same vertex, then it is called a Hamilton circuit. Hamiltonian: If a graph has a Hamilton circuit, then it is called a Hamiltonian. Calculation: The Hamilton circuit of K n is a complete graph with n vertices. According to the Hamilton theorem, each vertex of the Hamilton circuit is connected to the other vertex by an edge. For example, draw a tree diagram for the graph of K n by starting with a vertex A and is connected to other n - 1 vertices. So, there are n - 1 options for selecting the second vertex B. This second vertex has n - 2 options for selecting the third vertex since the first vertex A cannot be selected according Hamilton theorem. Similarly, the third vertex C has n - 3 options for selecting the next one and so on. So, the product of n consecutive numbers in a descending order is given by = n - 1 · n - 2 · n - 3 ·

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Chapter 4.2, Problem 45.2E

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Why there are n-1! in a Hamilton circuit of Kn.

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Chapter 4.2, Problem 45.1E

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Why there are n - 1 ! in a Hamilton circuit of K n .

To explain: Why there are n-1! in a Hamilton circuit of Kn.

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Chapter 4 Solutions

To explain:

Why there are n-1! in a Hamilton circuit of Kn.