User:Jason Kimberley/CDEall6

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

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

wiki			$\Delta$				A185131	A184941	A184951	A184961	A184971	A184981	A184991
$\Delta$	$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8	9	10	11
3	A068934	A005177	3			A179184	A002851	A006820	A006821	A006822	A014377	A014378	A014381	A014382	A014384
4	A186714	A186724	4			A185114	A014371	A033886	A058275	A058276	A181153	A181154	A181170
5	A186715	A186725	5			A185115	A014372	A058343	A205295
6	A186716	A186726	6			A185116	A014374	A058348
7	A186717	A186727	7			A185117	A014375
8	A186718	A186728	8			A185118	A014376
	A186719	A186729	9			A185119	A210709

A185131 is also tabulated by House of Graphs.

See also the Magma code of this index.

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

Index of sequences counting connected k-regular simple graphs with girth exactly g

		$\Delta$			A003982	A198303	A184940	A184950	A184960	A184970	A184980
$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8	9
A186733	A186743	3	A000004	A000004	A185013	A006923	A184943	A184953	A184963*	A184973*	A184983*	A184993*
A186734	A186744	4	A000004	A000004	A185014	A006924	A184944	A184954	A184964*	A184974*
A186735	A186745	5	A000004	A000004	A185015	A006925	A184945	A184955
A186736	A186746	6	A000004	A000004	A185016	A006926	A184946
	A186747	7	A000004	A000004	A185017	A006927
	A186748	8	A000004	A000004
		9	A000004	A000004

$g$	2	3	4	5	6	7
$\chi _{g\mathbb {N} }$	A059841	A079978	A121262	A079998	A079979	A082784

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

Index of sequences counting disconnected k-regular simple graphs with girth at least g

wiki			$\Delta$			A185220	A185230	A185240	A185250
$\Delta$	$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8	9	10	11
3	A068933	A068932	3	A157928	A157928	A165652	A165653	A033483	A165655	A165656	A165877	A165878	A185293	A185203	A185213
4	A185204	A185214	4	A157928	A157928	A185224	A185234	A185244	A185254	A185264*	A185274*	A185284*	A185294*
5	A185205	A185215	5	A157928	A157928	A185225	A185235	A185245*	A185255*
6	A185206	A185216	6	A157928	A157928	A185226	A185236	A185246*
7	A185207	A185217	7	A157928	A157928	A185227	A185237*
8		A185218	8	A157928	A157928	A185228	A185238*
		A185219	9	A157928	A157928	A185229

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

Index of sequences counting disconnected k-regular simple graphs with girth exactly g

	A210710	$\Delta$	lost :-( $\rightarrow$	A185010	A185020	A185030	A185040	A185050
$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8
A210703	A210713	3	A000004	A000004	A210723	A185033	A185043	A185053	A185063
A210704	A210714	4	A000004	A000004	A185024	A185034	A185044
A210705	A210715	5	A000004	A000004	A185025	A185035
A210706	A210716	6	A000004	A000004	A185026	A185036
	A210717	7	A000004	A000004	A185027	A185037
	A210718	8	A000004	A000004	A185028
		9	A000004	A000004	A185029

Notice that each sequence above is not the disconnected Euler transformation of the corresponding sequence counting connected k-regular simple graphs with girth exactly g: a disconnected graph with girth exactly g need only have one component with girth exactly g; the other component(s) only need have girth at least g.

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

Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

		$\Delta$			A026807	A185330	A185340
$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8
A051031	A005176	3	A000012	A000012	A008483	A005638	A033301	A165626	A165627	A165628	A180260
A185304	A185314	4	A000012	A000012	A008484	A185334	A185344	A185354	A185364
A185305	A185315	5	A000012	A000012	A185325	A185335
A185306	A185316	6	A000012	A000012	A185326	A185336
	A185317	7	A000012	A000012	A185327
	A185318	8	A000012	A000012	A185328
	A185319	9	A000012	A000012	A185329

* means identical to connected sequence for now because no intersection with disconnected.

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

Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

		$\Delta$			A026794	A185130	A185140
$\Delta$	$\Sigma$	$g$ \ $k$	0	1	2	3	4	5	6	7	8
A185643	A198313	3	A000004	A000004	A026796	A185133	A185143	A185153	A185163
A185644	A198314	4	A000004	A000004	A026797	A185134	A185144
A185645	A198315	5	A000004	A000004	A026798	A185135
A185646	A198316	6	A000004	A000004	A026799	A185136
	A198317	7	A000004	A000004	A026800
	A198318	8	A000004	A000004	A026801
		9	A000004	A000004	A026802

Notice that each sequence above is not the Euler transformation of the corresponding sequence counting connected k-regular simple graphs with girth exactly g: a disconnected graph with girth exactly g need only have one component with girth exactly g; the other component(s) only need have girth at least g.