A class of graphs for which the ulam conjecture holds

A median graph is a connected graph, such that for any three vertices u,ν and w there is exactly one vertex x that lies simultaneously on a shortest (u, ν)-path a shortest (ν, w)-path and a shortest (w, u)-path. It is proved that a median graph can be obtained from a one-vertex graph by an expansion procedure. From this characterization some nice properties are derived.