Berrachedi, A.; Mollard, M. Median graphs and hypercubes, some new characterizations. (English) Zbl 0933.05133 Discrete Math. 208-209, 71-75 (1999). 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. Cited in 2 Documents MSC: 05C75 Structural characterization of families of graphs Keywords:decomposition; partition; projection; antiprojection; characterizations; hypercubes; median graphs PDFBibTeX XMLCite \textit{A. Berrachedi} and \textit{M. Mollard}, Discrete Math. 208--209, 71--75 (1999; Zbl 0933.05133) Full Text: DOI