Geodesic
On enumeration of labelled connected graphs by the number of cutpoints
Diskretnaya Matematika, Tome 20 (2008) no. 1, pp. 52-63.

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We study the numbers $S_{mn}$ of labelled connected graphs with $n$ vertices among which $m$ are cutpoints. We obtain an explicit expression for the exponential generating function $S_m(z)$ of these numbers and find the asymptotics of the numbers $S_{mn}$ as $n\to\infty$ and $m=o(n)$. 
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V. A. Voblyi. On enumeration of labelled connected graphs by the number of cutpoints. Diskretnaya Matematika, Tome 20 (2008) no. 1, pp. 52-63. http://geodesic.mathdoc.fr/item/DM_2008_20_1_a3/

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