Parametric families of graphs | Regular graphs

Hamming graph

Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set Sd, the set of ordered d-tuples of elements of S, or sequences of length d from S. Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs Kq. 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. (Wikipedia).

Hamming graph
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Graph (discrete mathematics) | Hamming distance | Richard Hamming | Complete quadrangle | Hamiltonian path | Rook's graph | Hypercube graph | Vertex-transitive graph | Distance-regular graph | Regular graph | Unit distance graph | Cartesian product of graphs | Graph theory | Mathematics | Set (mathematics) | Vertex (graph theory) | Integer | Complete graph | Association scheme | Gray code | Tuple | Lattice graph