A343463 The number of connected graphs on n nodes that can be induced subgraphs of a Hamming graph.

1, 1, 2, 5, 11, 36, 117, 469, 2023

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.

Links

Table of n, a(n) for n=1..9.

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

Cf. A343464, A343162.

Sequence in context: A343162 A353210 A295495 * A130622 A112600 A156014

Adjacent sequences: A343460 A343461 A343462 * A343464 A343465 A343466

Keyword

nonn,more

Author

Don Knuth, Apr 16 2021

Status

approved