- #1

lemonthree

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I need to prove the above statement. I have a very strong gut feeling that the above equation is not true, and so I need to find a case where the graph diameter is greater than the average pairwise distance.

First off, I would like to clarify about the average pairwise distance, which is given below

Given that the denominator is C(n,2), I am assuming that the average pairwise distance will be taking the maximum number of edges? So in this case, the connected graph has edges connecting every single vertex to each other, always?

But how could this be? What if there was some vertex, $v_{1} $ and $v_{2} $ that is not connected?