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The concept of a median in a weighted graph is generalized to a multimedian. Then, it is shown that the optimum distribution of p switching centers in a communication network is at a p-median of the corresponding weighted graph. The following related problem in highway networks is also considered: What is a minimum number of policemen that can be distributed in a highway network so that no one is farther away from a policeman than a given distance d? This problem is attacked by generating all vertex-coverings (externally stable sets) of a graph by means of a Boolean function defined over the vertices of a graph. Then this idea is extended to Boolean functions that generate all matchings, all factors, and all possible subgraphs of G with given degrees.
S. L. Hakimi (Tue,) studied this question.