A tree has 10 vertices. How many edges does it contain?
Options
- A. 9
- B. 10
- C. 11
- D. More than one of the above
- E. None of the above
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Quiz Practice:
Correct Answer (Detailed Explanation is Below)
A. 9
Detailed Explanation
Every tree containing N vertices has N - 1 edges. Therefore, a tree with 10 vertices contains 10 - 1 = 9 edges. A tree is a connected acyclic graph. Removing any edge from a tree disconnects it, while adding an edge between two existing vertices creates exactly one cycle. Remember the important relationship: vertices = N, edges = N - 1.