login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181153 Number of connected 7-regular simple graphs on 2n vertices with girth at least 4. 14
1, 0, 0, 0, 0, 0, 0, 1, 1, 8, 741, 2887493 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

a(10) was computed by the author in 3 hours using GENREG on Dec 02 2009.

a(11) was computed by the author using GENREG over 45.7 processor days at U. Newcastle from Jan 25 to 27 2011.

REFERENCES

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.

LINKS

Table of n, a(n) for n=0..11.

Jason Kimberley, Connected regular graphs with girth at least 4

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

M. Meringer, Tables of Regular Graphs

EXAMPLE

The a(0)=1 null graph is vacuously 7-regular and connected; since it is acyclic then it has infinite girth.

The a(7)=1 graph is the complete bipartite graph K_{7,7} on 14 vertices.

The a(8)=1 graph has girth 4, automorphism group of order 80640, and the following adjacency lists:

01 : 02 03 04 05 06 07 08

02 : 01 09 10 11 12 13 14

03 : 01 09 10 11 12 13 15

04 : 01 09 10 11 12 14 15

05 : 01 09 10 11 13 14 15

06 : 01 09 10 12 13 14 15

07 : 01 09 11 12 13 14 15

08 : 01 10 11 12 13 14 15

09 : 02 03 04 05 06 07 16

10 : 02 03 04 05 06 08 16

11 : 02 03 04 05 07 08 16

12 : 02 03 04 06 07 08 16

13 : 02 03 05 06 07 08 16

14 : 02 04 05 06 07 08 16

15 : 03 04 05 06 07 08 16

16 : 09 10 11 12 13 14 15

CROSSREFS

7-regular simple graphs with girth at least 4: this sequence (connected), A185274 (disconnected), A185374 (not necessarily connected).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), this sequence (k=7), A181154 (k=8), A181170 (k=9).

Connected 7-regular simple graphs with girth at least g: A014377 (g=3), this sequence (g=4).

Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).

Sequence in context: A058921 A240283 * A184974 A060183 A145415 A204464

Adjacent sequences:  A181150 A181151 A181152 * A181154 A181155 A181156

KEYWORD

nonn,more,hard

AUTHOR

Jason Kimberley, last week of Jan 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified August 22 15:28 EDT 2014. Contains 245954 sequences.