2.4.2. Adding Edges to a Tree

Try these first

1. 1.

   What is the definition of a tree in graph theory?

   Hint

   Think about connectivity and cycles.

2. 2.

   How many edges are in a tree with 6 vertices?

   Hint

   Use the formula n-1.

3. 3.

   What does a tree have that makes it different from other graphs?

   • Multiple paths between vertices
   • No cycles allowed
   • It must have weights

   Hint

   Focus on the definition of a tree.

4. 4.

   Is a Minimum Cost Spanning Tree the same as any spanning tree?

   • True
   • False

   Hint

   Consider what makes a spanning tree minimum.

5. 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.

   Hint

   Always choose edges that keep you connected and cost-efficient.

6. 6.

   Provide a real-world example of a situation where Kruskal's algorithm might be more beneficial than Prim's algorithm.

   Hint

   Consider scenarios involving wireless networks or cable laying.