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Suppose u and v are two vertices in a graph G with ecc(u) = m, ecc(v)...

Suppose u and v are two vertices in a graph G with ecc(u) = m, ecc(v) = n. Prove: d(u, v) ≥ |m − n|.

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Answer #1

Without loss of generality, we assume that , otherwise, we will simply relabel the vertices and .

Since , so, there exists a vertex such that

Now,

Since , we obtain

Therefore, we have

Hence proved.

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