Median graphs and hypercubes, some new characterizations Original Research Article

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.