How many edges does a spanning tree of a graph with N vertices have?
Asked In: BPSC TRE 3.0Options
- A. N
- B. N-1
- C. N(N-1)/2
- 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. N-1
Detailed Explanation
A spanning tree of a connected graph containing N vertices always has exactly N - 1 edges. A spanning tree includes all vertices of the original graph, remains connected, and contains no cycle. In general, every tree with N vertices has N - 1 edges. If an additional edge is added to a tree, it creates a cycle. This property is fundamental to graph theory and minimum spanning tree algorithms.