Which statement about a spanning tree of a connected graph is correct?
Options
- A. It contains all vertices and N-1 edges
- B. It contains all edges of the graph
- C. It must contain at least one 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)
A. It contains all vertices and N-1 edges
Detailed Explanation
A spanning tree of a connected graph containing N vertices includes all N vertices and exactly N - 1 edges. It is connected and acyclic. It does not necessarily contain all edges of the original graph because extra edges can create cycles. A graph may have multiple different spanning trees, but every spanning tree of the same connected graph has the same number of vertices and edges.