A characterization of halved cubes

The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then it is proved that Qd is the only connected, d 2 -regular graph on 2d−1 vertices in which every edge lies in two d-cliques and two d-cliques do not intersect in a vertex.

• Type: Journal
• Year: 1998
• Where: ARSCOM
• Authors: Wilfried Imrich, Sandi Klavzar, Aleksander Vesel
• Keywords: ARSCOM 1998, Bipartition Vertex, Cube Qd, Halved Cube Qd