Eulerian and Semi-Eulerian - 12 Apps 2021

If you can trace a path around a network without repeating edges. This is said to be __________

A graph is Eulerian. This means it has ______

• 2 odd vertices

• All even vertices

• 3 even vertices

• No even vertices

Another graph is neither Eulerian or Semi-Eulerian. Select all that apply.

• It might have 1 odd vertices

• It might have 3 odd vertices

• It might have 2 odd vertices

• It might have all even vertices

A person walks down every road once exactly, but starts and ends at different houses. This means the graph has a _______

• Semi-Eulerian trail

• Eulerian trail

• Neither Semi-Eulerian or Eulerian trail

A person delivering newspapers starts at the depot, walks down every road exactly once and returns to the depot with an empty bag. This is an example of what type of graph?

• Eulerian

• Semi-Eulerian

• Neither Eulerian or Semi-Eulerian

Imagine 3 places, Alkimos, Baldivis and Coodanup are connected with roads. Each have 5 roads connecting to the other places. Is this network traversable?

• Yes

• No

Imagine 3 places, Alkimos, Baldivis and Coodanup are connected with roads. Each have 5 roads connecting to the other places. Which of the following is true:

• It is neither Eulerian or Semi-Eulerian

• It is Eulerian

• It is Semi-Eulerian

Look at the image. Decide which is true:

• It is neither Eulerian or Semi-Eulerian

• It is Eulerian

• It is Semi-Eulerian

Look at the image. Decide what is true:

• It is Eulerian because it has a Eulerian trail

• It is Semi-Eulerian because it has an open trail

• It is neither Eulerian or Semi-Eulerian

If a graph is Semi-Eulerian, where must you start and finish?

• Anywhere you like

• At an odd vertex

• At an even vertex