Given an undirected connected graph $G=(V, E)$. Find the induced subgraph $G[W]$ of $G$ with the largest diameter $d$, where the diameter is the largest distance between any pair of vertices.

The diameter of the graph below is 2, because we can get from every node to every other node over at most 2 edges. However, when removing a node, for example C (and it's adjacent edges), the diameter increases to 3, because we need 3 edges from A to E.

One possible solution would be to generate all subgraphs, calculate the diameter and select the largest. However, the number of subgraphs rises exponentially with the number of vertices, so this is infeasible.