First of all, for distinct weighted graph we can’t do bfs.
So what we can do for this,
Already we know for minimum weight spanning tree with V vertices,we have V-1 edges.Also to traverse adjacency list ,time complexity required is O(V+E) and here for V-1 edges we have O(V) time complexity.
So while traversing adjacency list of T, we can compare the newly added weight with the weights on the node .If the newly added weight is smaller then will be change in minimum weight spanning tree otherwise not.
So we can say time complexity is O(V)