A connected graph has 8 vertices and 12 edges. How many edges must be removed to obtain a spanning tree?
Options
- A. 3
- B. 4
- C. 5
- 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. 4
Detailed Explanation
A spanning tree of a graph with 8 vertices must contain exactly 8 - 1 = 7 edges. The original graph contains 12 edges, so the number of edges that must be removed is 12 - 7 = 5. Thus, the correct answer is actually 5, which corresponds to option C. Removing suitable edges must preserve connectivity while eliminating all cycles until only a spanning tree remains.