Practice Handshaking Theorem (24.1.6) - Graph Theory Basics - Discrete Mathematics

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6 sample questions

Question 1.
What is the degree of a vertex connected to 4 edges?
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The degree is simply the count of edges.
Question 2.
Can an undirected graph have an empty edge set? Why?
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Focus on the definition of a graph.
3Question 3.
What does the Handshaking Theorem state?
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Consider how vertices are related through edges.
4Question 4.
Does a self-loop contribute one or two to a vertex's degree?
- True
- False
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Recall the definition of degree.
Question 5.
Create a graph with 5 vertices where the degrees of vertices are 4, 3, 3, 2, and 1. Ensure the graph is undirected. Is there any violation of the Handshaking Theorem?
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Check the Handshaking Theorem for validation.
Question 6.
In a connected graph, if every vertex has an even degree, show how you can form an Eulerian circuit.
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Reflect on Euler's properties.

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