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

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

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

Δ A026794 A185130 A185140
Δ Σ 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.


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