So I'm kind of wondering if I'm correct on something relating to an algorithms class. Let's say I want to, for whatever reason, find the maximum spanning tree of a graph such that the edge weight is at maximum instead of minimum.
In addition, let's say I want to find a spanning tree with the maximum product-sum weight (the product of the edges of the spanning tree is at its maximum).
Assuming edge-weights must be greater than 0, would their spanning trees contain the same edges? I'm pretty sure that their spanning trees are equal.
Plus, I also believe that a modified Kruskal's algorithm searching for maximum weighted edges would create these spanning trees since you'd want the largest weights for both types of maximum trees.
Is my thinking correct?