A243247 Number of unlabeled, connected graphs on n vertices with at least one subgraph isomorphic to an open-bowtie graph.

0, 0, 0, 0, 10, 78, 755, 10709, 259123, 11703831, 1006591916, 164058548700, 50335887082115

Offset: 1

Author

Travis Hoppe and Anna Petrone, Jun 01 2014

Keywords

• nonn
• more

Examples

			n=5: The ten simple (no loop) graphs satisfying the cricket (open bowtie) subgraph condition have vertex degrees: 4^5, 4^3 3^2, 4^2 3^2 2, 4^2 2^3, 4 3^4, 4 3^3 1, 4 3^2 2^2, 4 3 2^2 1, 4 2^4 (bowtie), 4 2^2 1^2 (cricket). - _Wolfdieter Lang_, Jun 08 2025
		

Links

• Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
• T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014
• Eric Weisstein's World of Mathematics, Cricket Graph

Formula

a(n) = A001349(n) - A242791(n).

Extensions

a(11)-a(13) added using formula by Falk Hüffner, Jan 16 2016