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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 1ES

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.

**Given information:**

Given, graph is:

â€ƒâ€ƒ

**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 7 (A, B, C, D, E, F, G)

So the graph is Hamiltonian if the degree of every vertex is at least 7/2=3...

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