A294206 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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

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