folded hypercube graph

The folded n-cube graph, perhaps better termed "folded hypercube graph, " is a graph obtained by merging vertices of the n-hypercube graph Q_n that are antipodal, i.e., lie at a distance n (the graph diameter of Q_n). Brouwer et al. 1989 (p. 222) use the notation square _k for the folded k-cube graph. For n>2, the folded n-cube graph is regular of degree n. It has 2^(n - 1) vertices, 2^(n - 2) n edges, and diameter ⌊n/2⌋. The chromatic number is 2 for n even and 4 for n odd.

Clebsch graph | halved cube graph | hypercube graph | Kummer graph