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The median procedure on median graphs. (English) Zbl 0906.05023
An ordered k-tuple π=(x 1 ,,x k ) of elements of a finite metric space (X,d) is called a profile. An element xX for which i=1 k d(x,x i ) is minimum is called a median of π. The median procedure is the function Med(π)={xx is a median of π}. 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.

MSC:
05C12Distance in graphs