Sum of degrees in a graph $= 2 |E|$, as each edge contributes two to the sum of degrees. So, when sum of degrees are same, number of edges must also be same.
Trees with equal no of edges has to have equal no of vertices as No of Edges $=$ No of vertices $- 1$, in a tree.
So, should be $|S| = |T|$
Correct Answer: $C$