The t-median function on graphs

A median of a sequence π=x1,x2,…,xkπ=x1,x2,…,xk of elements of a finite metric space (X,d)(X,d) is an element x   for which ∑i=1kd(x,xi) is minimum. The function M with domain the set of all finite sequences on X   and defined by M(π)={x:xM(π)={x:x is a median of π}π} is called the median function on X  , and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π)M(π), 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.