I wonder if the following graph problems have been studied and have names.


**Problem(s).**
Given two $n$-vertex unlabeled graphs $G\_1$ and $G\_2$, find their maximum/minimum edge intersection. That is find two labeled graphs $H\_1 = ([n], E\_1)$ and $H\_2 = ([n],E\_2)$ such that $H\_1 \simeq G\_1$, $H\_2 \simeq G\_2$, and $|E\_1 \cap E\_2|$ is maximized/minimized.


It would also be helpful to know if these problems have been studied for special classes of graphs, e.g. for trees.



Maximum/minimum intersection of two graphs
This is essentially the [Maximum common edge subgraph problem](https://en.wikipedia.org/wiki/Maximum_common_edge_subgraph), which is at least as hard as the subgraph isomorphism problem.


