User:Jason Kimberley/C girth ge 4

girth	C	D	E
$\geq$	Cge	Dge	Ege
$=$	Ceq	Deq	Eeq

A186714:

Triangular array $C(n,k)=$ the number of connected $k$-regular graphs, having girth at least 4, with $n$ nodes, for $0\leq k\leq n/2$.

The $(k,4)$-cage is $K_{k,k}$.

These counts are the output from Markus Meringer's GENREG. The italicised values are from my running of GENREG at The University of Newcastle High Performance Computing Facility for the durations described in the column sequences.

Girth at least: 3 4 5 6 7 8

A186724	$n$			A185114	A014371	A033886	A058275	A058276	A181153	A181154	A181170
$\forall$	$k$	0	1	2	3	4	5	6	7	8	9	10
1	1	1
1	2	0	1
0	3	0	0
1	4	0	0	1
1	5	0	0	1
2	6	0	0	1	1
1	7	0	0	1	0
4	8	0	0	1	2	1
1	9	0	0	1	0	0
10	10	0	0	1	6	2	1
3	11	0	0	1	0	2	0
37	12	0	0	1	22	12	1	1
32	13	0	0	1	0	31	0	0
340	14	0	0	1	110	220	7	1	1
1608	15	0	0	1	0	1606	0	1	0
18020	16	0	0	1	792	16828	388	9	1	1
193907	17	0	0	1	0	193900	0	6	0	0
2867725	18	0	0	1	7805	2452818	406824	267	8	1	1
32674058	19	0	0	1	0	32670330	0	3727	0	0	0
1581632114	20	0	0	1	97546	456028474	1125022325	483012	741	13	1	1
6705889824	21	0	0	1	0	6636066099	0	69823723	0	1	0	0
	22	0	0	1	1435720	100135577747	3813549359274	14836130862	2887493		14	1
	23	0	0	1	0	1582718912968						0
	24	0	0	1	23780814
	25	0	0	1	0
	26	0	0	1	432757568
	27	0	0	1	0
	28	0	0	1	8542471494
	29	0	0	1	0
	30	0	0	1	181492137812
	31	0	0	1	0
	32	0	0	1	4127077143862

$C(23,10)=0$ was found using GENREG taking 33.3 processor days on 18th May 2011.