A294206 Triangle read by rows: T(n,k) = number of graphs on n nodes with domatic number k (n >= 1, 1 <= k <= n).

1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 11, 16, 5, 1, 1, 34, 66, 49, 5, 1, 1, 156, 415, 417, 49, 5, 1, 1, 1044, 4172, 5515, 1559, 49, 5, 1, 1, 12346, 66415, 135818, 58474, 1559, 49, 5, 1, 1, 274668, 1942352, 5671132, 3758169, 357232, 1559, 49, 5, 1, 1

Offset

1,4

Comments

The domatic number of a graph is the maximum number of disjoint dominating sets in a domatic partition of the graph.

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Domatic Number

Formula

T(n,1) = A000088(n-1).

T(n,n) = T(n,n-1) = 1.

Example

Triangle begins:
1
1,1
2,1,1
4,5,1,1
11,16,5,1,1
34,66,49,5,1,1
156,415,417,49,5,1,1
1044,4172,5515,1559,49,5,1,1

Crossrefs

Cf. A000088 (row sums and first column).

Sequence in context: A192404 A373746 A291261 * A332402 A263284 A332404

Adjacent sequences: A294203 A294204 A294205 * A294207 A294208 A294209

Keyword

nonn,tabl

Author

Eric W. Weisstein, Oct 24 2017

Extensions

Row 10 added by Eric W. Weisstein, Nov 03 2017

Status

approved