A289158 Number of unlabeled connected loopless multigraphs with n nodes of degree 4 or less and with at most double edges.

1, 1, 2, 7, 28, 112, 590, 3419, 23453, 178599, 1516692, 14083855, 142029043, 1542152723, 17925912574, 221938298129, 2914638247016, 40455853460661, 591654481313077, 9091698010380468, 146433114305147508, 2466517505722469501, 43361349681960337334

Offset: 0

Author

Natan Arie Consigli, Jul 04 2017

Keywords

• nonn

Comments

In chemical terms this counts the following molecules (excluding stereoisomers) without triple bonds, given n carbon atoms:

- carbon allotropes;

- aliphatic hydrocarbons;

- resonance structures of graphically non-equivalent anti-aromatic and aromatic hydrocarbons;

Some molecules are theoretical and may or may not exist.

Links

• Daniel R. Herber, Enhancements to the perfect matching approach for graph enumeration-based engineering challenges, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE 2020).

Crossrefs

Cf. A121941, A289157 (allows more than two edges), A303030, A303031.

Programs

nauty

geng -c -D4 ${n} -q | multig -m2 -D4 -u

Extensions

a(15)-a(22) from Andrew Howroyd, Mar 20 2020