The median procedure on median graphs
An ordered \(k\)-tuple \(\pi= (x_1,\dots, x_k)\) of elements of a finite metric space \((X, d)\) is called a profile. An element \(x\in X\) for which \(\sum^k_{i= 1}d(x, x_i)\) is minimum is called a median of \(\pi\). The median procedure is the function \(\text{Med}(\pi)= \{x\mid x\) is a median of \(\pi\}\). These concepts are studied in the case when \(X\) is the vertex set of a graph with the usual distance. In particular, they are studied for median graphs, i.e. connected graphs \(G\) in which for any three vertices \(x\), \(y\), \(z\) there is a unique vertex \(w\) on the geodesic between each pair of \(x\), \(y\), \(z\). Special attention is paid to cube-free median graphs.
scientific article; zbMATH DE number 1180361
scientific article