Exchange economy find core
Core Allocations are Pareto efficient allocations that must satisfy individual rationality i.e. these allocations must yield at least as much satisfaction to the individuals as their respective endowments. In the given question, core allocations are represented by line connecting $(e/2, e/2)$ to $(e,e)$.
Dashed line on the left graph is representing the set of efficient allocations and on the right graph is representing the Core allocations.