__Abstract__ A median (antimedian) of a profile of vertices on a graph $G$ is a vertex that minimizes (maximizes) the … remoteness value, that is, the sum of the distances to the elements in the profile. The median (or antimedian) function has as … antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In …

An antimedian of a profile $\\pi = (x_1, x_2, \\ldots , x_k)$ of vertices of a graph $G$ is a vertex maximizing the sum … of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on $G$ and … obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The …