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Use Dirac's theorem to verify that the graph is Hamiltonian. Then find a Hamiltonian circuit.
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Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
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Section
BuyFindarrow_forward
Mathematical Excursions (MindTap C...
4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 3ES
Textbook Problem
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Use Dirac's theorem to verify that the graph is Hamiltonian. Then find a Hamiltonian circuit.
To determine
To determine if the graph is Hamiltonian using Dirac's theorem. Then to find a Hamiltonian circuit.
Explanation of Solution
Given information:
Given, graph is:
  
Calculation:
Dirac's theorem states, for a connected graph with at least three vertices and no multiple edges, if the number of vertices is n and every vertex has degree of at least n/2, then the graph is a Hamiltonian graph.
Here,
The number of vertices in the graph is 8 (A, B, C, D, E, F, G, H)
So the graph is Hamiltonian if the degree of every vertex is at least 8/2=4
And,
The degree of the vertex A is 4
The degree of the vertex B is 4
The degree of the vertex C is 4
The degree of the vertex D...
Chapter 5 Solutions
Mathematical Excursions (MindTap Course List)
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addCh. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - A pen-tracing puzzle is given. See if you can find...Ch. 5.1 - Explain why the following pen-tracing puzzle is...Ch. 5.1 - Transportation An X in the table below indicates a...Ch. 5.1 - Transportation The table below shows the nonstop...Ch. 5.1 - Social Network A group of friends is represented...Ch. 5.1 - Baseball The local Little League baseball teams...Ch. 5.1 - Determine (a) the number of edges in the graph,...
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