2.4.4. Implications of Properties

Try these first

1. 1.

   Define a Minimum Cost Spanning Tree.

   Hint

   Think about the connection and cost aspects combined.

2. 2.

   What is the main property of a tree?

   Hint

   Reference the definition you learned earlier.

3. 3.

   What is the key property of Minimum Cost Spanning Trees?

   • They can have loops
   • They minimize edge costs
   • They are random in structure

   Hint

   Focus on cost efficiency.

4. 4.

   True or False: A tree can have more than n - 1 edges.

   • True
   • False

   Hint

   Recall the properties of a tree.

5. 5.

   Consider a weighted graph with 5 vertices and varying edge weights. Construct the MCST using Prim's and Kruskal's algorithms, showing your work.

   Hint

   Keep track of added edges and costs.

6. 6.

   Propose a strategy for using MCST in a supply chain management problem involving warehouses and transportation nodes.

   Hint

   Consider connectivity and minimizing resources similar to road restoration.