New Zealand
Level 7 - NCEA Level 2

# Euler Trails and Circuits

## Interactive practice questions

The following questions relate to Euler trails and circuits.

a

Which of the following is a correct description of an Euler trail?

A trail that passes through each edge of a graph exactly once.

A

A trail that starts and finishes at the same vertex.

B

A trail that passes through each edge of a graph at least once.

C

A trail that visits each vertex exactly once.

D

A trail that passes through each edge of a graph exactly once.

A

A trail that starts and finishes at the same vertex.

B

A trail that passes through each edge of a graph at least once.

C

A trail that visits each vertex exactly once.

D
b

Which of the following are correct descriptions of an Euler circuit? Select all that apply.

A circuit that passes through each edge of a graph exactly once.

A

An Euler trail that visits each vertex exactly once.

B

A circuit that passes through each edge of a graph at least once.

C

An Euler trail that starts and finishes at the same vertex.

D

A circuit that passes through each edge of a graph exactly once.

A

An Euler trail that visits each vertex exactly once.

B

A circuit that passes through each edge of a graph at least once.

C

An Euler trail that starts and finishes at the same vertex.

D
Easy
Approx 2 minutes

The following questions relate to Euler trails and circuits.

Suppose $G$G is a very large network, with $300$300 vertices, each of even degree.

Is it possible to draw an Euler trail on the following network?

### Outcomes

#### M7-5

Choose appropriate networks to find optimal solutions

#### 91260

Apply network methods in solving problems