   # 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. ### 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 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.

### Explanation of Solution

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.

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