This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352209 #8 Mar 15 2022 05:22:39
%S A352209 1,1,1,1,5,5,13,18,42
%N A352209 Largest number of maximal perfect node-induced subgraphs of an n-node graph.
%C A352209 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).
%F A352209 a(m+n) >= a(m)*a(n).
%F A352209 Limit_{n->oo} a(n)^(1/n) >= 42^(1/9) = 1.51482... .
%e A352209 All graphs with at most four nodes are perfect, so a(n) = 1 for n <= 4 and any graph is optimal.
%e A352209 All optimal graphs (i.e., graphs that have n nodes and a(n) maximal perfect subgraphs) for 5 <= n <= 9 are listed below. Since a graph is perfect if and only if its complement is perfect, the optimal graphs come in complementary pairs.
%e A352209 n = 5: the 5-cycle;
%e A352209 n = 6: the wheel graph with any subset of the spokes removed (8 graphs in total);
%e A352209 n = 7: the chestahedral graph and its complement;
%e A352209 n = 8: the bislit cube graph, the snub disphenoidal graph, and their complements;
%e A352209 n = 9: the bislit cube graph with an additional node with edges to two neighboring nodes of degree 4 and to the two nodes of degree 3 on the opposite face of the cube, the snub disphenoidal graph with an additional node with edges to the four nodes of degree 4, and their complements.
%Y A352209 Cf. A052431, A052433.
%Y A352209 For a list of related sequences, see cross-references in A342211.
%K A352209 nonn,more
%O A352209 1,5
%A A352209 _Pontus von Brömssen_, Mar 08 2022