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

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

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

		${\displaystyle \Delta }$			A026794	A185130	A185140
${\displaystyle \Delta }$	${\displaystyle \Sigma }$	${\displaystyle g}$ \ ${\displaystyle k}$	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.