The median function on median graphs and semilattices ?
A median of a k -tuple of vertices of a finite connected graph G is a vertex x for which 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(?)={x|x is a median of ?} 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.
primary 05c12 05c75 secondary 06a12 90a08