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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 33ES

Textbook Problem

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- Draw a connected graph with six vertices that has no Euler circuits and no Hamiltonian circuits.
- Draw a graph with six vertices that has a Hamiltonian circuit but no Euler circuits.
- Draw a graph with five vertices that has an Euler circuit but no Hamiltonian circuits.

To determine

**(a)**

To draw a connected graph with six vertices that has no Euler circuits and no Hamiltonian circuits.

**Given information:**

Given, a connected graph with six vertices that has no Euler circuits and no Hamiltonian circuits is to be drawn.

**Calculation:**

A graph is said to be connected if every vertex can be reached from any other vertex by following the edges.

A circuit (that starts and ends at the same vertex) is said to be an Euler circuit if it uses every edge but only once. (i.e...

To determine

**(b)**

To draw a graph with six vertices that has a Hamiltonian circuit but no Euler circuits.

To determine

**(c)**

To draw a graph with five vertices that has an Euler circuit but no Hamiltonian circuits.

Mathematical Excursions (MindTap Course List)

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