A287424 -id:A287424 - cp's OEIS frontend

A121941 Number of unlabeled connected simple graphs with n nodes of degree 4 or less.

1, 1, 1, 2, 6, 21, 78, 353, 1929, 12207, 89402, 739335, 6800637, 68531618, 748592936, 8788983173, 110201690911, 1468157196474, 20695559603921, 307590282700915, 4805537369573319, 78710267083015571, 1348394635886684901, 24109112440149231355, 449050443283294835914

Offset: 0

Parthasarathy Nambi, Sep 03 2006

Number of graphs of hydrogen bonded water clusters.
This counts the connected graphs where each vertex has degree 4 or less. - Charles R Greathouse IV, Jul 07 2017
Also number of saturated hydrocarbons and allotropes with n carbon, or valence 4, atoms (excluding stereoisomers) following the octet rule. - Natan Arie Consigli, Jul 07 2017

			With 4 carbons, n-butane, i-butane, cyclobutane, bicyclobutane, methylcyclopropane and tetrahedrane are the 6 isomers satisfying the property above, so a(4)=6. - _Natan Arie Consigli_, Jul 07 2017
If n=5 then the number of graphs of hydrogen bonded water clusters is 21.

G. Brinkmann, Generating water clusters and other directed graphs, J. Math. Chem. 46 (4) (2009) 1112-1121, Table 1.
T. Miyake and M. Aida, Enumeration of topology-distinct structures of hydrogen bonded water clusters, Chem. Phys. Lett., vol. 363 (2002) pp. 106-110. See Table 1 column 2 on page 109.

Cf. A121942, A243393 (degree 3 or less), A287424 (excludes allotropes), A289157, A289158, A303032 (degree 5 or less).

nauty
```
geng -c -D4 ${n} -q | multig -m1 -D4 -u
```

More terms sent by Natan Arie Consigli, Jul 07 2017
Renamed by Andrew Howroyd, Mar 19 2020 based on comment by Charles R Greathouse IV.
a(16)-a(24) from Andrew Howroyd, Mar 19 2020

A289159 Number of unlabeled connected simple graphs with n nodes of degree 4 or less, except trees and 4-regular graphs.

Original entry on oeis.org

0, 0, 1, 4, 17, 72, 342, 1905, 12156, 89268, 738911, 6798758, 68520038, 748502910, 8788173335, 110193643134, 1468070949946, 20694573672876, 307578336064984, 4805384561143819, 78708210390090371, 1348365584611572634, 24108682771962822336, 449043803118075490633

Offset: 1

Natan Arie Consigli, Jul 07 2017

nonn

Also number of saturated cyclic hydrocarbons (cycloalkanes and alkyl cycloalkanes) with n carbon atoms satisfying the octet rule. Stereoisomerism is not taken into account. Some of the drawn structures may or may not exist due to their strained geometries.

Cf. A000602, A006820, A121941, A287424.

a(n) = A121941(n) - A006820(n) - A000602(n).

a(n) = A287424(n) - A000602(n).

a(0) removed and a(16)-a(24) from Andrew Howroyd, Mar 20 2020

cp's OEIS Frontend

A121941 Number of unlabeled connected simple graphs with n nodes of degree 4 or less.

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