Vertex fusion under diameter constraints

Given a graph G = ( V , E ) , a positive integer k, and a positive integer d, we want find a subset V k with k vertices such the graph obtained by identifying the vertices from V k in G has diameter at most d. We prove that for every d ⩾ 2 the problem is NP-complete. For the case of trees we provide a polynomial time algorithm that exploits the relationship with the r-dominating set problem.