Abstract
A median of a profile of vertices (a sequence of vertices) on a connected graph is a vertex that minimizes the sum of the distances to the elements in the profile. The median function has as output the set of medians of a profile. Median function is an important consensus function for the location of a desirable facility in a network. The axiomatic characterization of the median function is studied by several authors on special classes of graphs like trees and median graphs. In this paper, we determine the median sets of all types of profiles and obtain an axiomatic characterization for the median function on block graphs, an immediate generalization of trees.KeywordsProfilesBlock graphMedian setsMedian functionAxiomatic characterization
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