For $d \geq 1$ determine: $$ \max_{\text{diam}(G) = d} \min \{\text{diam}(T): \, T \, \text{spanning tree of} \, G \} $$
I'm having trouble understanding what this quantity represents. Does this suppose to mean that for every $d$ we find the minimum diameter of $G$'s spanning trees and then the maximum diameter of all those minima?
Can someone explain this in simple words and provide me with a hint on how to find it?