A332407 Number of simple graphs on n unlabeled nodes with upper domination number greater than independence number.

0, 0, 0, 0, 0, 1, 6, 85, 2574, 193486

Offset

1,7

Comments

The upper domination number of a graph is the maximum cardinality of a minimal dominating set. For any graph the upper domination number is greater than or equal to the independence number. This sequence gives the number of graphs where it is strictly greater than.

The m X n rook graphs with 2 <= m < n are a class of graph with this property because the independence number is m, and a row of n rooks is minimally dominating.

Links

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Independence Number

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Eric Weisstein's World of Mathematics, Rook Graph

Example

The a(6) = 1 graph illustrated below has independence number 2 and upper domination number 3.
    *--------o
    | \    / |
    |  *--o  |
    | /    \ |
    *--------o
The above graph is the 2 X 3 rook graph, drawn to show all edges.
The three vertices marked with an asterisk are a minimal dominating set.

Crossrefs

Cf. A263341, A332403.

Sequence in context: A381243 A064329 A187740 * A358297 A209035 A384981

Adjacent sequences: A332404 A332405 A332406 * A332408 A332409 A332410

Keyword

nonn,more

Author

Andrew Howroyd, Feb 15 2020

Status

approved