Hamming graph

In some cases, Hamming graphs may be considered more generally as the Cartesian products of complete graphs that may be of varying sizes. Unlike the Hamming graphs H(d,q), the graphs in this more general class are not necessarily distance-regular, but they continue to be regular and vertex-transitive.

Special cases

• H(2,3), which is the generalized quadrangle G Q (2,1)
• H(1,q), which is the complete graph K_q
• H(2,q), which is the lattice graph L_q,q and also the rook's graph
• H(d,1), which is the singleton graph K₁
• H(d,2), which is the hypercube graph Q_d. Hamiltonian paths in these graphs form Gray codes.
• Because Cartesian products of graphs preserve the property of being a unit distance graph, the Hamming graphs H(d,2) and H(d,3) are all unit distance graphs.