Let T be a graph. Suppose there is a unique path between every pair of vertices...

Let T be a graph. Suppose there is a unique path between every pair of vertices in T. Prove that T is a tree.

Can I do this using the contraposative? Like Let u,v be in T and since I am assuming T to not be a tree this allows cycles to occur thus the paths must not be unique. Am I on the right track?

Expert Solution

Yes your approach is right. I have given two proofs one by normal method and one by contrapositive.

Colby Messinger answered 2 years ago

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