construct Hamming graph
string of distinct characters
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 qd 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.
H32 ≔ HammingGraph⁡3,2
H32≔Graph 1: an undirected graph with 8 vertices and 12 edge(s)
H53 ≔ HammingGraph⁡5,3
H53≔Graph 2: an undirected graph with 243 vertices and 1215 edge(s)
The GraphTheory[SpecialGraphs][HammingGraph] command was introduced in Maple 2023.
For more information on Maple 2023 changes, see Updates in Maple 2023.
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