User:Jason Kimberley/D k-reg girth eq g index

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.