On a Relation between ψ-Centroid and ψ-Blocks in a Graph

摘要

The problem of finding the location of the cen- ter and the problem of finding the median in a graph are im- portant and basic among many network location problems. In connection with these two problems, the following two theorems are well-known. One is proved by Jordan and Sylvester, and it shows that the center of every tree consists of either one vertex or two adjacent vertices. The other is proved by Jordan and it shows that the centroid (median) of every tree consists of ei- ther one vertex or two adjacent vertices.