Given a graph and the number of groups we want to divide the graph into, Find the best way to divide the graph, such the max diameter of all the groups is minimum
The graph is undirected, the number of nodes in each of groups(or sub-graphs) may not necessarily be the same.
This is NP-complete, by reduction of the clique cover problem : graphs of diameter 1 are cliques, and deciding whether there's a partition of a given graph into $k$ cliques is NP-complete.
If instead of diameter you were looking for radius, it would be NP-complete by reduction of the dominating set problem (where the radius = 1).