Practice Number Of Edges In A Tree (2.4.1) - Minimum Cost Spanning Trees

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8 questions

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6 sample questions

Question 1.
What defines a tree in graph theory?
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Think about how trees are different from other graphs.
Question 2.
If a tree has 7 vertices, how many edges does it have?
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Use the formula: n - 1.
3Question 3.
What relationship exists between the number of vertices and edges in a tree?
- n - 1 edges
- n + 1 edges
- n edges
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Think about the definition of a tree.
4Question 4.
True or False: A tree can have cycles.
- True
- False
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Recall the properties of a tree.
Question 5.
Given a graph with 8 vertices and a total of 12 edges, can it be a tree? Justify your answer.
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Use the definition of trees.
Question 6.
Construct a minimum spanning tree for a weighted graph shown below: (provide a sample graph with weights). Describe how you would apply Prim's Algorithm.
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Visualize the steps of adding edges without making a cycle.

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