Hamming graph

Hamming graph

Hamming graphs are a special class of graphs used in several branches of mathematics 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.

The special case in which "q" = 2 is also known as the hypercube graph, denoted "Qd". The special cases in which "d" = 1 and "d" = 2 are the complete graph and rook's graph, respectively.

The Hamming graphs are interesting in connection with error-correcting codes and association schemes, to name two areas.


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