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

Author

Andrew Howroyd, Feb 15 2020

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A263341, A332403.