The Hamming graph H(d, q), sometimes also denoted q^d, is the graph Cartesian product of d copies of the complete graph K_q. H(d, q) therefore has q^d vertices. H(d, q) has chromatic number q and graph diameter d. Hammin graphs are distance-regular and geomtric . Special cases are summarized in the following table. H(1, q) | complete graph K_q H(2, 3) | generalized quadrangle G Q(2, 1) H(2, q) | rook graph L_(q, q) H(d, 1) | singleton graph K_1 H(d, 2) | hypercube graph Q_d

complete graph | Doob graph | Hamming code | Hamming distance | hypercube graph | rook graph | xyz embedding