Practice Euler's Theorem (24.1.7) - Graph Theory Basics - Discrete Mathematics - Vol 2
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Euler's Theorem

Practice - Euler's Theorem

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define what a vertex and an edge are.

💡 Hint: Think of a graph as a network of points.

Question 2 Easy

What is the degree of a vertex?

💡 Hint: Count how many edges touch a vertex.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Euler's Theorem state?

The sum of the degrees is odd.
The number of vertices with odd degree is even.
Every graph must have at least one edge.

💡 Hint: Think about the implications for vertex counts.

Question 2

True or False: A graph can have any number of odd-degree vertices.

True
False

💡 Hint: Recall Euler's theorem.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a graph with 5 vertices and 5 edges, demonstrate Euler's theorem by identifying vertices with odd and even degrees.

💡 Hint: What must the total reflect about odd counts?

Challenge 2 Hard

Devise a simple graph that satisfies Euler's theorem with at least 6 vertices.

💡 Hint: Sketch different configurations!

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Reference links

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