Exam-style question
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Explain the difference between a tree and a rooted tree. Include the meaning of root, parent, child and descendant in your answer.
Model answer
What a good answer should say
- A tree is a connected, undirected graph with no cycles, and it does not have to have a root.
- A rooted tree is a tree in which one vertex has been designated as the root.
- The root is the only node with no parent.
- The other nodes have parent-child relationships, and all of them are descendants of the root.
Explanation
Why this works
The key distinction is that a root is not required in a general tree but is designated in a rooted tree. Once a root is chosen, parent-child relationships can be described.
The root has no parent, while every other node is a descendant of it.
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