A385929 Number of simple, undirected, prime graphs G on n unlabeled vertices with no degree-1 vertex in G or its complement, as well as having no induced P5 in G or in its complement.

0, 0, 0, 0, 1, 0, 0, 1, 9, 142

Offset: 1

Author

Jim Nastos and Clara Elliott, Jul 12 2025

Keywords

• nonn
• more

Comments

Here, "prime" means with respect to modular decomposition (see link). A P5 is a path on 5 vertices.

Examples

			The only such graph on n=5 is the C5. The only such graph on n=8 is the split graph called the 4-sun (see the House of Graphs link).
		

Links

• The House of Graphs, 4-sun graph
• Wikipedia, Modular decomposition.

Crossrefs

Cf. A079473, A385693, A385697.