A303030 -id:A303030 - cp's OEIS frontend

A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

1, 3, 4, 12, 22, 68, 166, 534, 1589, 5464, 18579, 68320, 255424, 1000852, 4018156, 16671976, 70890940, 309439942, 1381815168, 6310880471, 29428287639, 140012980007, 678970863717, 3353545264060, 16857749613964, 86191265140699, 447951112379963, 2365177154077186

Offset: 1

Nico Van Cleemput, Jun 04 2014

nonn

a(n) is also the number of isomorphism classes of connected loopless multigraphs with n vertices of degree 3 or less. - Andrew Howroyd, Mar 20 2020

Nino Bašić and Ivan Damnjanović, On cubic polycirculant nut graphs, arXiv:2411.16904 [math.CO], 2024. See p. 22.
Gunnar Brinkmann, Nico Van Cleemput, and Tomaž Pisanski, Generation of various classes of trivalent graphs, Theoretical Comp. Sci. (2013) Vol. 502, 16-29.

Column k=3 of A334546.

Cf. A000421, A243392, A243393, A243394, A303030.

a(23)-a(28) from Andrew Howroyd, Mar 20 2020

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

Original entry on oeis.org

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

Natan Arie Consigli, Jul 04 2017

nonn

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.

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).

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

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

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

A303033 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single, double or triple edges.

Original entry on oeis.org

1, 1, 3, 12, 81, 535, 5274, 60684, 869238, 14595645, 284939257, 6347472749, 159579271688, 4482770916274, 139578090353236, 4783834092385411, 179397242557917048, 7322223973235272082, 323760818899998259561, 15443359560966718348986, 791699492870169123493379

Offset: 0

Natan Arie Consigli, Jun 04 2018

nonn

Cf. A134818, A303030, A303031, A303032.

for n in {1..11}; do geng -c -D5 ${n}  -q | multig  -m3 -D5 -u;

a(12)-a(20) from Andrew Howroyd, Mar 20 2020

cp's OEIS Frontend

A243391 Number of isomorphism classes of connected 3-regular loopless multigraphs with n vertices and with semi-edges allowed.

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

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nauty

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A303033 Number of unlabeled connected loopless multigraphs with n nodes of degree 5 or less and with single, double or triple edges.

Views

Author

Keywords

Crossrefs

Programs

nauty

Extensions