Antipodal metrics and split systems
A metric \(d\) on a finite set \(X\) is called antipodal if there exists a map \(\sigma: X \rightarrow X\) so that \(d(x,\sigma(x))= d(x,y) + d(y,\sigma (x))\) holds for all \(x,y \in X.\) In this paper the authors examine antipodal metrics that are in addition totally split decomposable and give explicit characterization of such metrics.
scientific article; zbMATH DE number 1740608