On embedding complete graphs into hypercubes

An embedding of Kn into a hypercube is a mapping of the n vertices of Kn to distinct vertices of the hypercube, and the associated cost is the sum over all pairs of (mapped) vertices of the Hamming distance between the vertices. Let f(n) denote the minimum cost over all embeddings of Kn into a hypercube (of any dimension). In this note we prove that f(n) = (n 1)2, unless n = 4 or n = 8, in which case f(n) = (n 1)2

• Type: Journal
• Year: 1998
• Where: DM
• Authors: Michael Klugerman, Alexander Russell, Ravi Sundaram
• Keywords: Associated Cost, DM 1998, Embedding, Hypercube