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The median procedure on median graphs. (English) Zbl 0906.05023
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.

05C12Distance in graphs
Full Text: DOI Link
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