OFFSET
1,3
COMMENTS
A Hamming graph is a Cartesian product of complete graphs. Each vertex is named by a sequence of coordinates. Two vertices are adjacent if they differ in exactly one coordinate. The induced subgraph need not preserve distance, only adjacency.
REFERENCES
D. E. Knuth, The Art of Computer Programming, Volume 4B (in preparation). Section 7.2.2.3 will have an exercise devoted to this topic.
EXAMPLE
For n=4 the a(4)=5 graphs are: P4 (000,100,110,111); C4 (00,10,11,01); K31 [the claw] (000,100,010,001); K4\P3 [the paw] (00,10,01,02); K4 (00,01,02,03).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Don Knuth, Apr 16 2021
STATUS
approved