A112426 Number of connected simple graphs with n vertices, n+6 edges, and vertex degrees no more than 4.

0, 0, 0, 0, 0, 1, 9, 134, 1714, 18436, 167703, 1327240, 9372119, 60324933, 359730035, 2012733260, 10670975762, 54028108819, 262872075003, 1235323112178, 5630370812614

Offset: 1

Author

Jonathan Vos Post, Dec 21 2005

Keywords

• nonn
• more

Comments

Distribution of carbon skeletons. See the paper by Hendrikson and Parks for details. If n=6 the number of 7-cyclic skeletons is 1. If n=7 the number of 7-cyclic skeletons is 9. If n=10 the number of 7-cyclic skeletons is 18436. - Parthasarathy Nambi, Jan 05 2007

Links

• J. B. Hendrickson and C. A. Parks, Generation and Enumeration of Carbon skeletons, J. Chem. Inf. Comput. Sci., 31 (1991), 101-107. See Table 2, column 7 on page 103.
• Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs [gives different numbers for n > 10].

Crossrefs

The analogs for n+k edges with k = -1, 0, ..., 7 are: A000602, A036671, A112410, A112619, A112408, A112424, A112425, this sequence, A112442. Cf. A121941.

Programs

nauty

for n in {6..13}; do geng -c -D4 ${n} $((n+6)):$((n+6)) -u; done # Andrey Zabolotskiy, Nov 24 2017

Extensions

New name, offset corrected, and a(11)-a(14) corrected by Andrey Zabolotskiy, Nov 24 2017

a(15)-a(21) added by Georg Grasegger, Jun 05 2023