The t-median function on graphs

A median of a sequence pi = x1, x2, … , xk of elements of a finite metric space (X, d ) is an element x for which ∑ k, i=1 d(x, xi) is minimum. The function M with domain the set of all finite sequences on X and defined by M(pi) = {x: x is a median of pi} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(pi), a generalization of the median function is introduced and studied on various graphs and ordered sets. In addition, new results are presented for median graphs.