An upper bound is given on the minimum distance between $i$ subsets
of the same size of a regular graph in terms of the $i$-th largest
eigenvalue in absolute value. This yields a bound on the diameter in
terms of the $i$-th largest eigenvalue, for any integer $i$. Our
bounds are shown to be asymptotically tight. A recent result by
Quenell relating the diameter, the second eigenvalue, and the girth
of a regular graph is obtained as a byproduct.
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