The median function on median graphs and semilattices Original Research Article

A median of a k-tuple π=(x1,…,xk) of vertices of a finite connected graph G is a vertex x for which ∑i=1kd(x,xi) is minimum, where d is the geodesic metric on G. The function M with domain the set of all k-tuples with k>0 and defined by M(π)={x | x is a median of π} is called the median function on G. In this paper a new characterization of the median function is given for G a median graph. This is used to give a characterization of the median function on median semilattices.