T is a graph with n vertices. T is connected and has exactly n−1 edges, then:
2005
T is a graph with n vertices. T is connected and has exactly n−1 edges, then:
- A.
T is a tree
- B.
T contains no cycles
- C.
Every pair of vertices in T is connected by exactly one path
- D.
All of these
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Correct answer: D
A connected graph with n vertices and exactly n−1 edges satisfies the definition of a tree. Consequently, it has no cycles and unique paths between vertices, validating all specific options provided.
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