The t-median function on graphs
Fred R. McMorris, Henry Martyn Mulder, Robert Powers · RePub (Erasmus University Rotterdam) · 2005
A median of a sequence π = 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(π) = {x: x is a median of 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), 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.