The number of edges in a subgraph of a Hamming graph Original Research Article

Let G be a subgraph of the Cartesian product Hamming graph (Kp)r with n vertices. Then the number of edges of G is at most (View the MathML source)(p − 1) logpn, with equality holding if and only G is isomorphic to (Kp)s for some s ≤ r.