For any two vertices in a connected graph, there is:A. Exactly one path between themB. At least one path between themC. No path between themD. Multiple paths between them
Question
For any two vertices in a connected graph, there is:A. Exactly one path between themB. At least one path between themC. No path between themD. Multiple paths between them
Solution
The correct answer is B. At least one path between them. In a connected graph, there is always at least one path between any two vertices. This is by definition of a connected graph. However, there may be more than one path between two vertices, so saying there is exactly one path (option A) is not always true. Option C is incorrect because in a connected graph, there is never a case where there is no path between two vertices. Option D could be true in some cases, but not all, so it is not the best answer.
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