

A112410


Number of connected simple graphs with n vertices, n+1 edges, and vertex degrees no more than 4.


7



0, 0, 0, 1, 5, 17, 56, 182, 573, 1792, 5533, 16977, 51652, 156291, 470069, 1407264, 4193977, 12451760, 36838994, 102733261
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

Such graphs are also referred to (e.g., by Hendrickson & Parks) as carbon skeletons with two rings, or bicyclic skeletons, although actual number of simple cycles in such graphs can exceed 2 (e.g., in the example).  Andrey Zabolotskiy, Nov 24 2017


LINKS

Table of n, a(n) for n=1..20.
J. B. Hendrickson and C. A. Parks, Generation and Enumeration of Carbon skeletons, J. Chem. Inf. Comput. Sci., 31 (1991), 101107. See Table 2, column 2 on page 103.
Michael A. Kappler, GENSMI: Exhaustive Enumeration of Simple Graphs.


EXAMPLE

The only such graph for n = 4 is:
oo
/
oo


PROG

(nauty/bash)
for n in {4..15}; do geng c D4 ${n} $((n+1)):$((n+1)) u; done # Andrey Zabolotskiy, Nov 24 2017


CROSSREFS

The analogs for n+k edges with k = 1, 0, ..., 7 are: A000602, A036671, this sequence, A112619, A112408, A112424, A112425, A112426, A112442. Cf. A121941 (any number of edges), A006820 (2n edges), A125669A125673.
Sequence in context: A081495 A191645 A146240 * A146271 A145371 A112044
Adjacent sequences: A112407 A112408 A112409 * A112411 A112412 A112413


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Dec 08 2005


EXTENSIONS

Corrected offset and new name from Andrey Zabolotskiy, Nov 20 2017


STATUS

approved



