Practice References (1.3) - Euler Path and Euler Circuit - Discrete Mathematics

Practise this section

9 questions

Flashcard drill
5 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define Euler Circuit.
Show hintHide hint
Think about circuits and where they start and end.
Question 2.
What is needed for an Euler Path to exist?
Show hintHide hint
Consider what happens when a vertex has an odd number of edges.
3Question 3.
What defines an Euler Circuit?
- Visits every edge once and ends at a different vertex
- Visits every edge once and returns to the starting vertex
- Only visits some edges
Show hintHide hint
Think about the shape it makes.
4Question 4.
Can a graph with all vertices of odd degree have an Euler Circuit?
- True
- False
Show hintHide hint
Recall the conditions for Euler paths and circuits.
Question 5.
Given a connected multigraph with vertices of degrees 4, 4, 2, and 2, is it possible to form an Euler Circuit? Justify your answer.
Show hintHide hint
Verify the degrees of all vertices.
Question 6.
Create a graph with five vertices where two have odd degrees and demonstrate an Euler path using Fleury's algorithm.
Show hintHide hint
Think about how edges connect these vertices.

5 more questions in this section. Enroll free to practise them all.