A317722 -id:A317722 - cp's OEIS frontend

A380805 Number of unlabeled simple connected graphs with n nodes of degree at most 3 and each node a member of exactly one cycle.

1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 7, 10, 18, 27, 49, 81, 147, 256, 476, 858, 1612, 2991, 5676, 10729, 20575, 39423, 76232, 147602, 287518, 561195, 1100190, 2161552, 4261059, 8418035, 16675006, 33098322, 65844566, 131233923, 262066375, 524224509, 1050414569

Offset: 0

Gordon Hamilton, Feb 23 2025

nonn

All such graphs are cactus graphs (with bridges allowed).

Andrew Howroyd, Table of n, a(n) for n = 0..1000
Wikipedia, Cactus graph.
Index entries for sequences related to cacti.

Row sums of A380633.

Cf. A000083, A001349, A317722, A380632 (nodes of any degree).

Vec(G(40)) \\ G() defined in A380633. - Andrew Howroyd, Feb 24 2025

a(13) onwards from Andrew Howroyd, Feb 24 2025

A381468 Number of simple connected graphs on n unlabeled nodes with no node a member of more than one cycle.

Original entry on oeis.org

1, 1, 1, 2, 4, 8, 20, 48, 133, 374, 1124, 3439, 10923, 35245, 116128, 387729, 1312038, 4485906, 15486546, 53900520, 188998450, 667062919, 2368440477, 8454560144, 30328595227, 109285433191, 395425965732, 1436219868659, 5234881134074, 19143123415166, 70216752517419

Offset: 0

Andrew Howroyd, Feb 24 2025

nonn

All such graphs are cactus graphs (with bridges allowed).

Andrew Howroyd, Table of n, a(n) for n = 0..1000
R. J. Mathar, Counting connected graphs without overlapping cycles, arXiv:1808.06264 [math.CO] (2018).
Wikipedia, Cactus graph.
Index entries for sequences related to cacti.

Row sums of A381467.

Cf. A000083, A317722 (with 2-cycles), A380632, A380805.

PARI
```
Vec(G(31,1)) \\ G() defined in A381467.
```

cp's OEIS Frontend

A380805 Number of unlabeled simple connected graphs with n nodes of degree at most 3 and each node a member of exactly one cycle.

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