5.3.1. Checking for Cycles

Try these first

1. 1.

   What is a minimum cost spanning tree?

   Hint

   Think about the total weights of connecting all nodes.

2. 2.

   What does Kruskal's algorithm start with?

   Hint

   Consider the importance of edge weights in the algorithm.

3. 3.

   What is the first step in Kruskal's algorithm?

   • Add edges to the spanning tree
   • Sort all edges by weight
   • Check for cycles

   Hint

   Remember the order of operations in Kruskal's algorithm.

4. 4.

   True or False: Kruskal's algorithm can result in cycles in the spanning tree.

   • True
   • False

   Hint

   Think about how the algorithm maintains tree properties.

5. 5.

   Given a weighted graph with the following edges and weights: { (A, B, 1), (B, C, 2), (A, C, 3), (C, D, 4) }, apply Kruskal's algorithm to determine the minimum spanning tree and calculate its total weight.

   Hint

   Start by sorting edges based on their weights.

6. 6.

   Consider a graph where there are 6 vertices and 7 edges. If you apply Kruskal's algorithm, what is the maximum number of edges you can add to the spanning tree without creating a cycle?

   Hint

   Recall the property of trees regarding edges and vertices.