In this paper we give a new and self-contained proof of the following theorem: Let G denote some finite connected and bipartite graph. If in addition for any two vertices x, y the subgraph induced on those vertices lying on some geodesic from x to y is antipodal, then G is a hypercube of some dimension. © 2002 Elsevier Science B.V. All rights reserved.
Wenzel, W. (2002). A sufficient condition for a bipartite graph to be a cube. Discrete Mathematics, 259(1–3), 383–386. https://doi.org/10.1016/S0012-365X(02)00543-5