A352213 Largest number of maximal cographical node-induced subgraphs of an n-node graph.

1, 1, 1, 4, 10, 12, 23, 38, 64

Offset: 1

Author

Pontus von Brömssen, Mar 08 2022

Keywords

• nonn
• more

Comments

This sequence is log-superadditive, i.e., a(m+n) >= a(m)*a(n). By Fekete's subadditive lemma, it follows that the limit of a(n)^(1/n) exists and equals the supremum of a(n)^(1/n).

Examples

			All graphs with at most three nodes are cographs, so a(n) = 1 for n <= 3 and any graph is optimal.
All optimal graphs (i.e., graphs that have n nodes and a(n) maximal cographical subgraphs) for 4 <= n <= 9 are listed below. Since a graph is a cograph if and only if its complement is a cograph, the optimal graphs come in complementary pairs.
  n = 4: the path of length 3 (self-complementary);
  n = 5: the 5-cycle (self-complementary);
  n = 6: the Hajós graph (also known as a Sierpiński sieve graph) and its complement;
  n = 7: the elongated triangular pyramid and its complement;
  n = 8: the Möbius ladder and its complement (the antiprism graph);
  n = 9: the pentagonal bipyramid with an additional path of length 3 between the two apex nodes (self-complementary).
		

Crossrefs

Cf. A000084, A000669.

For a list of related sequences, see cross-references in A342211.

Formula

a(m+n) >= a(m)*a(n).

Limit_{n->oo} a(n)^(1/n) >= 64^(1/9) = 1.58740... .