Traversability

Which of these graphs is Eulerian (traversable)?

(NB. A traversable graph can be drawn without removing your pencil from the paper, without tracing the same edge twice and it starts and finishes at exactly the same point.)

• Graph 1

• Graph 2

• Graph 3

Which of these graphs is non-Eulerian (non-traversable)?

(NB. A non-traversable graph cannot be drawn without removing your pencil from the paper or without tracing the same edge twice.)

• Graph 1

• Graph 2

• Graph 3

What type of graph is Graph 2?

• Eulerian (traversable)

• Semi-Eulerian (semi-traversable)

• Non-Eulerian (non-traversable)

Which of the following statements about Eulerian (traversable) graphs is true?

• The start and finish vertices are the same

• The start and finish vertices are different

• It is not possible to draw it without removing your pencil from the paper

• It is not possible to draw it without tracing the same edge more than once

Which one of the following statements about semi-Eulerian (semi-traversable) graphs is true?

• The start and finish vertices are the same

• The start and finish vertices are different

• It is not possible to draw it without removing your pencil from the paper

• It is not possible to draw it without tracing the same edge more than once

Which of the following statements about Eulerian (traversable) graphs is true?

• All vertices have even degree (valency)

• Exactly two vertices have even degree (valency)

• Exactly two vertices have odd degree (valency)

• There are more than two vertices of odd degree (valency)

Which of the following statements about semi-Eulerian (semi-traversable) graphs is true?

• All vertices have even degree (valency)

• Exactly two vertices have even degree (valency)

• Exactly two vertices have odd degree (valency)

• There are more than two vertices of odd degree (valency)

Which of the following statements about non-Eulerian (non-traversable) graphs is true?

• All vertices have even degree (valency)

• Exactly two vertices have even degree (valency)

• Exactly two vertices have odd degree (valency)

• There are more than two vertices of odd degree (valency)

Which one of these statements is a consequence of the fact that the sum of the degrees (valencies) of the vertices in a graph is always even?

• The number of vertices with even valency must be even

• The number of vertices with even valency must be odd

• The number of vertices with odd valency must be even

• The number of vertices with odd valency must be odd

This vertices in this network have degrees

2, 4, 4, 2, 4, 4, 4

Is the graph Eulerian, semi-Eulerian or non-Eulerian?

• Eulerian

• Semi-Eulerian

• Non-Eulerian