The t-median function on graphs
A median of a sequence ?=x1,x2,,xk ? = x 1 , x 2 ,  , x k of elements of a finite metric space (X,d) ( X , d ) is an element x  for which ? i = 1 k d ( x , x i ) is minimum. The function M with domain the set of all finite sequences on X  and defined by M(?)={x:x M ( ? ) = { x : x is a median of ?} ? } is called the median function on X , and is one of the most studied consensus functions. Based on previous characterizations of median sets M(?) M ( ? ) , 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.
primary 06a12 secondary 05c75