demi-cube | demi-cube graph | demicube | demicube graph | half cube graph | half-cube | half-cube graph | halved cube

Let Y_n denote the graph with vertex set V(X_n), where X_n is the n-hypercube and two vertices are adjacent in Y_n iff they are at distance 1<=d<=2 in X_n. Y_n is therefore the graph square of the hypercube graph Q_(n + 1)/2. Y_n is not connected, but it contains two isomorphic components on 2^(n - 1) vertices, each of which is called a halved n-cube graph, half cube graph, the halved n-cube, or sometimes the n-demi-cube graph. The most common notation is 1/2 Q_n, but Steinerberger uses Q_(2)^n.

16-cell | Clebsch graph | error-correcting code | folded cube graph | halved graphs | hypercube graph