   # Use Dirac's theorem to verify that the graph is Hamiltonian. Then find a Hamiltonian circuit. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### 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...

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