What happens when one edge is removed from a tree?
Options
- A. It remains connected
- B. It becomes disconnected
- C. It necessarily creates a cycle
- D. More than one of the above
- E. None of the above
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Quiz Practice:
Correct Answer (Detailed Explanation is Below)
B. It becomes disconnected
Detailed Explanation
A tree is minimally connected, meaning every edge is important for maintaining connectivity. If any one edge is removed from a tree, the tree becomes disconnected, producing two separate components. This property is called the bridge property of tree edges. Conversely, adding an edge between two vertices of a tree creates exactly one cycle. These properties are useful in graph algorithms and network design.