Abstract: In the pcenter problem, p facilities are located in the network such that the maximum weighted distance from a client to its nearest facility is minimized. If all client weights are equal to 1, it is called an unweighted center problem. Unweighted 1-center problem is studied on block graphs with a unit edge length. It is shown that the problem can be solved in linear time using the tree structure of a block graph.

Key words: block graph, center problem, location problems, networks