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Center function identifies vertices on a graph which minimizes the maximum distance to a set of input vertices. Axiomatic approach attempts to uniquely distinguish location functions such as center, median and mean functions using a set of axioms. In this paper, an attempt is made to find an axiomatic characterization of center function on crown graphs using both universal and nonuniversal axioms.

A mean of a sequence π = (x₁, x₂, …, x_k) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean (π) = {x|x is a mean of π} is called the mean function on X. In this note, the mean function on finite trees is characterized axiomatically.

An antimedian of a profile π = (x₁, x₂, …, x_k) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on G and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The 'converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for two classes of graphs on which the antimedian is well behaved: paths and hypercubes.

A median of a sequence π = (x₁, x₂, …, x_k) of elements of a finite metric space (X, d) is an element x for which is minimum. The function with domain the set of all finite sequences on X and defined by Med(π) = {x | x is a median of π} is called the Median function on X. In this note, an axiomatic characterization of the median function on finite trees is given.