HammingGraph(d,q) returns the Hamming graph, an undirected graph whose vertices correspond to sequences of symbols of length d chosen from some alphabet of size q.

The graph has $q^d$ vertices, each of which corresponds to a sequence of the $q$ symbols of length $d$. Two vertices are connected if the corresponding sequences differ pairwise by a single symbol, that is, if their Hamming distance is 1.

HammingGraph(d,s) returns a Hamming graph equivalent to HammingGraph(d,length(s)) but whose vertices are strings of length q composed from the characters in s.

The graph is named for Richard Hamming.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$\mathrm{H32}≔\mathrm{HammingGraph}\left(3\,2\right)$

$\mathrm{H32}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 8\; vertices\; and\; 12\; edge(s)}$

$\mathrm{DrawGraph}\left(\mathrm{H32}\right)$

$\mathrm{H53}≔\mathrm{HammingGraph}\left(5\,3\right)$

$\mathrm{H53}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 243\; vertices\; and\; 1215\; edge(s)}$

$\mathrm{NumberOfEdges}\left(\mathrm{H53}\right)$

$1215$

The GraphTheory[SpecialGraphs][HammingGraph] command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.