Vertex k-center problem

The Vertex \( k \)-center problem is a classical problem in combinatorial optimization and graph theory. In this problem, you are given an undirected graph \( G = (V, E) \) and an integer \( k \). The objective is to select \( k \) vertices (also known as centers) from the graph such that the maximum distance from any vertex in the graph to the nearest selected center is minimized.