Hamming graphs are a special class of graphs used in several branches of mathematics and computer science. In Mathematics and Computer science, a graph is the basic object of study in Graph theory. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their Let S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set S^d, 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. In Mathematics and Computer science, a graph is the basic object of study in Graph theory.

The special case in which q = 2 is also known as the hypercube graph, denoted Q_d. In the mathematical field of Graph theory, the Hypercube graph Qn is a Regular graph with 2 n The special cases in which d = 1 and d = 2 are the complete graph and rook's graph, respectively. In the mathematical field of Graph theory, a complete graph is a Simple graph in which every pair of distinct vertices is connected by an In Graph theory, a rook's graph (also called a lattice graph) is a graph that represents all legal moves of the rook Chess piece on

The Hamming graphs are interesting in connection with error-correcting codes and association schemes, to name two areas. In Mathematics, Computer science, Telecommunication, and Information theory, error detection and correction has great practical importance in In Mathematics, association schemes are structures that appear in many different forms in the fields of Combinatorics and Statistics.

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