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I'm looking for bounds on diameter of a given undirected graph with $n$ vertices and $m$ edges? Formally, I look to find $D_{min}$ and $D_{max}$ such that: $D_{min}\leq Diamter\leq D_{max}$ and it is possible to construct a graph (with $n$ vertices and $m$ edges) satisfying the equalities. A trivial bound is $1\leq Diameter\leq n-1$. Thank you.

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This paper might be of interest to you: math.ucsd.edu/~fan/mypaps/fanpap/107diameters.pdf –  Joseph Malkevitch Apr 17 '12 at 15:48

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