2.4. Properties of Trees

Try these first

1. 1.

   What defines a tree in graph terms?

   Hint

   Think about cycles and connectivity.

2. 2.

   Is a tree allowed to have cycles?

   Hint

   Recall the definition of a tree.

3. 3.

   What characterizes a spanning tree?

   • It has cycles
   • It spans all vertices with minimum edges
   • It can be disconnected

   Hint

   Consider the definition of a spanning tree.

4. 4.

   A tree can have more than one path between any two vertices.

   • True
   • False

   Hint

   Recall the unique path property of trees.

5. 5.

   Given the following weighted graph, identify both Prim's and Kruskal's Minimum Cost Spanning Trees. Provide the steps taken.

   Hint

   Work carefully through each step to ensure clarity in your choices.

6. 6.

   Explain a scenario in which using MST would be critical for infrastructure development.

   Hint

   Think about both financial and logistical efficiencies.