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Median graphs and hypercubes, some new characterizations. (English) Zbl 0933.05133

Summary: A projection (antiprojection respectively) of a vertex \(x\) of a graph \(G\) over a subset \(S\) of vertices is a vertex of \(S\) at a minimal (maximal respectively) distance from \(x\). Which graphs are such that there is uniqueness of the antiprojection or uniqueness of the projection of a vertex over intervals or convex sets? We study these four properties and obtain new characterizations of hypercubes and median graphs.

MSC:

05C75 Structural characterization of families of graphs
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