Practice Adding Edges To A Tree (2.4.2) - Minimum Cost Spanning Trees - Design & Analysis of Algorithms

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the definition of a tree in graph theory?
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Think about connectivity and cycles.
Question 2.
How many edges are in a tree with 6 vertices?
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Use the formula n-1.
3Question 3.
What does a tree have that makes it different from other graphs?
- Multiple paths between vertices
- No cycles allowed
- It must have weights
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Focus on the definition of a tree.
4Question 4.
Is a Minimum Cost Spanning Tree the same as any spanning tree?
- True
- False
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Consider what makes a spanning tree minimum.
Question 5.
Given a graph with 5 vertices and edges of varying costs. How would you implement Prim's algorithm to find the MCST? Illustrate the steps sequentially.
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Always choose edges that keep you connected and cost-efficient.
Question 6.
Provide a real-world example of a situation where Kruskal's algorithm might be more beneficial than Prim's algorithm.
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Consider scenarios involving wireless networks or cable laying.

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