OFFSET
0,21
LINKS
Jan Goedgebeur and Jorik Jooken, Exhaustive generation of edge-girth-regular graphs, arXiv:2401.08271 [math.CO], 2024. See p. 12.
EXAMPLE
a(0)=0 because even though the null graph (on zero vertices) is vacuously 4-regular and connected, since it is acyclic, it has infinite girth.
The a(19)=1 graph is the unique (4,5) cage: the Robertson graph (see also A159191). It has the following adjacency lists.
01 : 02 03 04 05
02 : 01 06 07 08
03 : 01 09 10 11
04 : 01 12 13 14
05 : 01 15 16 17
06 : 02 09 12 15
07 : 02 10 13 16
08 : 02 11 14 17
09 : 03 06 13 17
10 : 03 07 14 18
11 : 03 08 16 19
12 : 04 06 16 18
13 : 04 07 09 19
14 : 04 08 10 15
15 : 05 06 14 19
16 : 05 07 11 12
17 : 05 08 09 18
18 : 10 12 17 19
19 : 11 13 15 18
CROSSREFS
4-regular simple graphs with girth exactly 5: this sequence (connected), A185045 (disconnected), A185145 (not necessarily connected).
Connected k-regular simple graphs with girth exactly 5: A006925 (k=3), this sequence (k=4), A184955 (k=5).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Feb 14 2011
STATUS
approved